Assessment of improvement of extension of reach of 10 … · Assessment of improvement of extension of reach ... seja suﬁcientemente alta ... 2.1 Introduction to GPON

Assessment of improvement of extension of reach

of 10 Gbps PONs by using APDs

Joao Adriano Ramalho Mourato

Thesis to obtain the Master of Science Degree in

Electrical and Computer Engineering

Supervisor: Prof. Dr. Adolfo da Visitacao Tregeira Cartaxo

Examination Committee

Chairperson: Prof. Dr. Jose Eduardo Charters Ribeiro da Cunha SanguinoSupervisor: Prof. Dr. Adolfo da Visitacao Tregeira CartaxoMembers of the Committee: Prof. Paula Raquel Laurencio

July 2015

ii

Acknowledgements

This dissertation would not have been possible without the support and encouragement of many

people throughout my education, whether explicitly mentioned here or not, and to these people

I express my sincere appreciation.

Firstly, I would like to express my deepest gratitude to my supervisor Associate Professor

Adolfo Cartaxo for the high quality of his academic advice and direction, and for his generous

help, patience and support throughout the development of this dissertation.

I would like to thank my family for all the love and unequivocal support they always gave

me and keep giving. Without your support and understanding I would never have been able to

finish this dissertation. This work is dedicated to you: Margarida Conceicao Ribeiro Ramalho

and Antonio Mao de Ferro Mourato. I also dedicate this work to sibling, Antonio Mourato.

Last, but by no means least, I would like to thank all my friends, without your encour-

agement, patience and example this dissertation would not have materialized. Luıs Mendes,

Joao Rafael, Pedro Freitas, Frederico Alcobia and Joao Augusto for all the good moments and

support you have provided to me along my graduation and master courses. Thank you all.

iii

iv

Abstract

The 10 gigabit per second passive optical network (XG-PON) standard was proposed to be em-

ployed in optical fibre telecommunication systems due to the increase in binary rate, possibility

of more users in the same PON and non-intrusive deployment on the existing optical access net-

work. The PON systems can use the Positive-Intrinsic-Negative diode (PIN) or the Avalanche

Photodiode (APD) as photodetector. However, the high bitrate increases the effect of the mode

partition noise (MPN). Therefore, the study of the photodetector performance in the presence

of the MPN is of special concern.

In this dissertation, the models that characterize the APD and MPN are described and their

impact on the performance of 10 Gbps PON is assessed through numerical computation. In

addition, for optimizing the performance of the APD on the XG-PON system, for non-null ex-

tinction ratio, an expression for the APD sensitivity is proposed.

The XG-PON, comprising the use of multi-longitudinal mode (MLM) lasers or single lon-

gitudinal mode (SLM) lasers at the optical line termination (OLT) and the optical network unit

(ONU), is evaluated. For a dispersion parameter value of 18.41 ps/(nm.km) in the downstream

and a dispersion parameter value of ´3.68 ps/(nm.km) in the upstream, MLM lasers cannot

be used in either direction. Moreover, the effect of the MPN on the signal from SLM lasers

is negligible, provided that the side-mode suppression ratio (SMSR) is high (SMSR ě 30 dB).

Furthermore, the average power level emitted by the ONU imposes a limit in the splitting ratio

and maximum distance.

Keywords: XG-PON, avalanche photo-diode, mode partition noise, multi-longitudinal

mode laser, single-longitudinal mode laser.

v

vi

Resumo

Foi proposta, em sistemas de telecomunicacoes por fibra optica, a rede optica passiva a 10

gigabits por segundo (XG-PON) para aumentar o ritmo binario, permitir mais utilizadores na

mesma PON e por ser facil a introducao nas redes de acesso existentes. Pode ser usado o

positivo-intrınseco-negativo (PIN) ou o fotodıodo de avalanche (APD) como fotodetector. No

entanto, o aumento do ritmo binario aumenta tambem o efeito do ruıdo de particao de modos

(MPN). Consequentemente, o estudo do desempenho do receptor na presenca de MPN e de

especial interesse.

Nesta dissertacao, descrevem-se os modelos que caracterizam APD e MPN e o seu impacto

no desempenho de sistemas de PON a 10 Gbps e avaliado atraves de calculos numericos. Alem

disso, e proposta uma expressao para a sensibilidade que tem em conta a razao de extincao, com

o objectivo de optimizar o impacto do APD no sistema XG-PON.

A XG-PON, contemplando o uso de lasers multimodo (MLM) e monomodo (SLM) como

emissores na terminacao optica de linha (OLT) e na unidade optica de rede (ONU), e avaliada.

Para um valor de parametro de dispersao de 18.41 ps/(nm.km) no sentido descendente e ´3.68

ps/(nm.km) no sentido ascendente, os lasers MLM nao podem ser utilizados. Ainda, o efeito

do MPN no sinal produzido por lasers SLM e desprezavel, desde que a razao de supressao do

modo lateral (SMSR) seja suficientemente alta (SMSR ě 30 dB). A potencia de emissao da

ONU e o factor limitativo na distancia maxima e numero de utilizadores.

Palavras-chave: XG-PON, foto-dıodo de avalanche, ruıdo de particao de modos, laser

multimodo, laser monomodo.

vii

viii

Table of Contents

Acknowledgements iii

Abstract v

Resumo vii

Table of Contents ix

List of Figures xiii

List of Tables xv

List of Acronyms xvii

List of Symbols xxi

1 Introduction 1

1.1 Scope of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Optical access networks . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 XG-PON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Objectives and structure of the dissertation . . . . . . . . . . . . . . . . . . . . 4

1.4 Main original contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Characterization of the XG-PON 7

2.1 Introduction to GPON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 XG-PON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Solutions for transmitter and receiver . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

ix

TABLE OF CONTENTS

2.3.2 Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 APD impact on the system performance 19

3.1 Motivation for using an APD . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Principles of APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Signal characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4 Receiver characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Noise characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5.1 Thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5.2 Shot noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 APD receiver sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.7 APD improvement over PIN . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.8 Analysis of sensitivity variation . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.9 Optimum avalanche gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 MPN impact on the system performance 41

4.1 Basic concepts of semiconductor lasers . . . . . . . . . . . . . . . . . . . . . 41

4.2 Characterization of MPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3 MPN modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3.1 Mode-partition coefficient . . . . . . . . . . . . . . . . . . . . . . . . 46

4.3.2 Mode-partition noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.4 MPN in MLM lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.5 MPN in SLM lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.6 Penalty for using a MLM laser . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.7 Penalty for using a SLM laser . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Assessment of XG-PON reach improvement 57

5.1 Link budget of the XG-PON system . . . . . . . . . . . . . . . . . . . . . . . 57

5.2 Improvement using MLM lasers . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.2.1 Downstream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.2.2 Upstream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

x

TABLE OF CONTENTS

5.3 Improvement using SLM lasers . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3.1 Downstream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3.2 Upstream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6 Conclusion and future work 67

6.1 Final conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

References 71

A APD receiver sensitivity with finite extinction ratio 75

A.1 Bit error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.2 Preparatory steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

A.3 Deriving APD sensitivity expression . . . . . . . . . . . . . . . . . . . . . . . 79

A.4 APD sensitivity applied to PIN . . . . . . . . . . . . . . . . . . . . . . . . . . 81

A.5 Deriving the APD optimum gain . . . . . . . . . . . . . . . . . . . . . . . . . 81

B Auxiliary derivations related to MPN 85

B.1 BER in SLM lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

B.1.1 BER particular cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

B.2 BER in SLM lasers based on Gaussian approximation . . . . . . . . . . . . . . 93

B.2.1 BER derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.3 Validation of the model used to obtain BER . . . . . . . . . . . . . . . . . . . 98

xi

TABLE OF CONTENTS

xii

List of Figures

2.1 GPON system example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 GPON and XG-PON coexistence example, assuming every ONU has a WDW

filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 XG-PON possible OLT-ONU pairs, according to the XG-PON power budgets. . 16

3.1 Avalanche photo-diode reach-through schematic. . . . . . . . . . . . . . . . . 20

3.2 Optical receiver structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Variation of the excess noise factor with avalanche gain for several values of kA. 26

3.4 Sensitivity improvement by using APD instead of a PIN diode. . . . . . . . . . 30

3.5 Sensitivity improvement by using APD instead of a PIN diode for three values

of extinction ratio for kA “ 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 30





3.8 Sensitivity variation with the avalanche gain for Ge, InGaAs and Si APDs. . . . 33

3.9 Sensitivity variation with the effective noise bandwidth value for kA “ 0.45 and

r “ 0.152. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.10 Sensitivity variation with the ionization coefficient ratio value for Be,n “ 8 GHz

and r “ 0.152. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.11 Sensitivity dependence on the extinction ratio value Be,n “ 8 GHz and kA “ 0.45. 36

3.12 Sensitivity versus sensitivity approximation, with extinction ratio r “ 0.05. . . 37

3.13 Sensitivity versus sensitivity approximation, with extinction ratio r “ 0.1. . . . 38

3.14 Sensitivity versus sensitivity approximation, with extinction ratio r “ 0.152. . . 38

4.1 Random power spectrum at different times t1, t2, for illustrating the partition

noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

xiii

LIST OF FIGURES

4.2 Power penalty when using a MLM laser in function of β parameter, for various

values of kMPN for Q“ 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Power penalty when using a MLM laser in function of β parameter, for various

values of kMPN for Q“ 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4 Relation between the increased power at the receiver and the side-mode sup-

pression ratio, considering a reference BER of 10´12 and r “ 0.1, for M “ 1

and M “ 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5 Relation between the increased power at the receiver and the side-mode sup-

pression ratio, considering a reference BER of 10´12 and M “ 10, for r “ 0.01,

r “ 0.1 and r “ 0.152. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

A.1 Sensitivity values for both solutions presented. . . . . . . . . . . . . . . . . . . 81

A.2 Sensitivity expression compared against its three components for an extinction

ratio of 0.152 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83


ratio of 0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83


ratio of 0.05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

B.1 Regions of integration of PpI ą ID0q. . . . . . . . . . . . . . . . . . . . . . . . 87

B.2 Region of integration of PpI ă ID1q. . . . . . . . . . . . . . . . . . . . . . . . 88

B.3 Gaussian distribution and noncentral Chi-squared distribution for ψ“ 2ˆ10´4 . 99

B.4 Gaussian distribution and noncentral Chi-squared distribution for ψ“ 5.0625ˆ

10´4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

xiv

List of Tables

2.1 Summary of GPON and XG-PON common characteristics. . . . . . . . . . . . 14

2.2 Summary of XG-GPON power budgets. . . . . . . . . . . . . . . . . . . . . . 15

3.1 Set of typical values for sensitivity parameters . . . . . . . . . . . . . . . . . . 29

3.2 Set of typical values for APD receivers . . . . . . . . . . . . . . . . . . . . . . 32

4.1 Parameters used for obtaining numeric results. . . . . . . . . . . . . . . . . . . 54

5.1 Typical parameters of XG-PON system used for obtaining numerical results. . . 59

5.2 Typical G.652 fibre parameters used for obtaining numerical results [34]. . . . 59

5.3 PON split ratios and corresponding losses [35]. . . . . . . . . . . . . . . . . . 59

5.4 Receiver parameters used for obtaining numerical results. . . . . . . . . . . . . 59

5.5 Sensitivities used for obtaining numerical results. . . . . . . . . . . . . . . . . 60

5.6 Emmiting powers for the optical sources of OLT and ONU using MLM and

SLM lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.7 Maximum distance imposed by the power budget and system margin for L“ 20

km, for both PIN and APD receivers as function of the splitter ratio without

FEC, in the downstream direction. . . . . . . . . . . . . . . . . . . . . . . . . 63


km, for both PIN and APD receivers as function of the splitter ratio using FEC,

in the downstream direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63


km, for both PIN and APD receivers as function of the splitter ratio without

FEC, in the upstream direction. . . . . . . . . . . . . . . . . . . . . . . . . . . 64


km, for both PIN and APD receivers as function of the splitter ratio using FEC,

in the upstream direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

xv

LIST OF TABLES

5.11 Summary of usable splitting ratios for L“ 20 km. . . . . . . . . . . . . . . . . 65

A.1 Set of typical values for sensitivity parameters for testing the two sensitivity

solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

xvi

List of Acronyms

Acronym Description

AES Advanced Encryption Standard

AGC Automatic gain control

APD Avalanche photo-diode

APON ATM Passive Optical Network

ATM Asynchronous Transfer Mode

BER Bit Error Ratio

BPON Broadband Passive Optical Network

CAS Client Adaptation Layer

CO Central Office

DBA Dynamic Bandwidth Allocation

DBRu Dynamic Bandwidth Report Upstream

DML Directly Modulated Laser

EFM Ethernet in the First Mile

EML Externally Modulated Laser

EPON Ethernet Passive Optical Network

FP Fabry-Perot

FEC Forward Error Correction

FS Framing Sublayer

xvii

LIST OF ACRONYMS

FSAN Full Service Access Network

FTTH Fibre To The Home

GEM GPON Encapsulation Method

GPON Gigabit Passive Optical Network

GTC GPON Transmission Convergence

HEC Header Correction Code

HSI High Speed Internet

ID Identification

IEEE Institute of Electrical and Electronics Engineers

IP Internet Protocol

ITU International Telecommunications Union

LED Light Emitting Diode

MAC Medium Control Access

MIB ONU Management Base

MLM Multi-longitudinal Mode

MSR Mode-Suppression Ratio

MPN Mode Partition Noise

NRZ Non-Return-to-Zero

ODN Optical Distribution Network

OLT Optical Line Terminal

OMCC ONU Management Control Channel Protocol

OMCI ONU Management Control Interface

ONU Optical Network Unit

PAS PHY Adaptation Sublayer

xviii

LIST OF ACRONYMS

PCBd Physical Control Block Downstream

PHY Physical

PIN Positive-Intrinsic-Negative

PLOAM Physical Layer Operations Administration Maintenance

PLOu Physical Layer Overhead Upstream

PMD Physical Medium Dependent

PON Passive Optical Network

POTS Plain Old Telephone Service

PSBd Physical Synchronization Block Downstream

PSBu Physical Synchronization Block Upstream

QoS Quality Of Service

RMS Root-Mean-Square

SLM Single Longitudinal Mode

SMF Single Mode Fibre

SMSR Side-mode Suppression Ratio

SNR Signal-To-Noise Ratio

TC Transmission Convergence

T-Cont Transmission Container

TDM Time Division Multiplexing

TDMA Time Division Multiple Access

VoIP Voice Over IP

WDM Wavelength-Division Multiplexing

xix

LIST OF ACRONYMS

xx

List of Symbols

Symbol Designation

αMPN power penalty induced by mode partition noise

η quantum efficiency

λ optical wavelength

λ0 optical wavelength of central partition mode

λi optical wavelength of ith partition mode

µ Gaussian distribution mean

ν central frequency of the optical spectrum

σ spectral width

σ0 root square variance of bit 0

σ1 root square variance of bit 1

σ2c thermal noise variance

σGaussian variance of Gaussian distribution

σ2mm variance of the main mode

σ2MPN mode partition noise variance

σn total noise root square variance at receiver

σ2s shot noise variance

σ2s,0 shot noise variance for bit 0

σ2s,1 shot noise variance for bit 1

σ2sm variance of the side mode

σ2T variance of the total current after the receiver

∆λ spacing between partition modes

∆τi relative delay of the ith partition mode

ψ non-central Chi-squared parameter

xxi

LIST OF SYMBOLS

b drop-out rate

B bit rate

Be,n effective noise bandwidth

c speed of light in vacuum

ci normalized amplitude of ith partition mode

dB decibel

Dλ fibre dispersion parameter

erf(¨) error function

erfc(¨) complementary error function

FApMq excess noise factor

Fn circuit noise figure

g semiconductor laser gain coefficient

GAPD gain of apd versus a pin

h Planck’s constant

I0 average bit 0 current

I1 average bit 1 current

Id dark current

ID receiver’s decision threshold current

Imc total multiplied current

Imm current of the main mode

Ip primary unmultiplied current

Ism current of the side mode

IT totl current after the receiver

xxii

LIST OF SYMBOLS

kA ionization coefficient ratio

kB Boltzmann’s constant

kMPN mode partition noise coefficient

L fibre length

Llayer semiconductor laser active-layer length

M avalanche gain

MOptimum optimal avalanche gain

nptq total noise voltage

nGptq Gaussian noise voltage

nexpptq exponential noise voltage

N total number of mode partition modes

pi minimum total incident power

pimode total incident power of ith partition mode

pi,0 incident power for bit 0

pi,1 incident power for bit 1

piPIN minimum total incident power for a PIN diode

PD receiver’s decision threshold power

Pmm single longitudinal mode laser main mode power

Psm single longitudinal mode laser most dominant side mode power

Psmpλiq measured time-average power spectrum of ith partition mode

ptotal total power of signal

q electron charge

Q Q parameter

r extinction ratio

rptq total pulse random response

r0 total pulse random response measured at sample time t0

xxiii

LIST OF SYMBOLS

Rλ unity gain responsivity

RλAPD avalanche gain responsivity

Rext extinction ratio in dB

RL load resistor

T temperature

yiptq partial pulse random response of ith partition mode

xxiv

Chapter 1

Introduction

In this chapter, it is presented an introduction to optical networks, with focus on the last part of

the network, between the user and the service provider, the access network. In section 1.1, the

scope of the work is presented, along with the brief history of the passive optical networks. In

section 1.2, it is presented the motivation for the development of this dissertation. Section 1.3

shows the objectives and structure of this dissertation. Lastly, in section 1.4, the main original

contributions of this dissertation are described.

1.1 Scope of the work

XG-PON has been proposed as an improvement to the deployed PON system, it allowed for

greater bandwidth, users and reach. The scope of this work is to assess the reach improvement

of XG-PON by using single-mode lasers (SLM) or multi-mode lasers (MLM), avalanche pho-

todiodes (APD), and the impact of the Mode Partition Noise (MPN) on the whole system and

its components.

This section presents the principles that support this work: the evolution of the optical ac-

cess networks and the history of Gigabit passive optical network (GPON) technology. The 10

Gigabit PON (XG-PON) is also introduced, in which the work will be focused.

1.1.1 Optical access networks

The evolution of telecommunications technologies and its rapid spread led to a remarkable

growth in the number of applications and services available to the users, resulting in dramatic

increase of demanded bandwidth. Thus, it was necessary to come up with a different approach

1

1. INTRODUCTION

in all segments of the network, in order to satisfy such demand. Focusing on the first mile (also

known as the access network), and in the new generation network technologies, the natural

course of action is to migrate (when possible) from copper solutions towards fibre solutions,

enabling the network to meet the demand. With that purpose in mind, the concept of Pas-

sive Optical Networks (PON) emerged in the mid 90s when the Full Service Access Network

(FSAN) group started working on fibre to the home (FTTH) architectures.

The International Telecommunications Union (ITU) later standardized the PON in its

G.983 recommendation, being the first draft based on Asynchronous Transfer Mode (ATM),

known as ATM PON (APON). However, due to various improvements and the decrease of the

use of ATM as a protocol, the final version of the recommendation came to be commonly re-

ferred as broadband PON (BPON), avoiding the close association with the ATM protocol. Later

in 2001, the FSAN started the development of an enhanced standard that could support multiple

services in their native form, improve the total bandwidth and its efficiency, upgrade the security

and management mechanisms in an evolutionary form. The result was the G.984 recommenda-

tion, also known as GPON.

Around the same time, the Institute of Electrical and Electronics Engineers (IEEE) formed

a task force named Ethernet in the first mile (EFM), which purpose was, as the name states;

bring Ethernet protocol into the access network. The group focused in several areas the most

relevant to our context being the Ethernet over point-to-multipoint fibre (EPON) that was rati-

fied as the IEEE 802.3ah in 2004.

Though progress were made with these technologies, the bandwidth demands of new ap-

plications adding to the increase of users, were, once again, pushing the need for more develop-

ments in the previous presented technologies, in order for them to provide bigger downstream

and upstream rates (per user) as well as extending the reach of the PON, etc. Therefore, recently,

extensions to the above-presented standards were added, resulting in the 10G-EPON ratified in

2009 as 802.3av and the XG-PON (or 10G-PON) as the ITU-T G.987 recommendation, on

which this work will be focusing.

1.1.2 XG-PON

The XG-PON inherits all requirements from the GPON, with a few additions. Also, it must

coexist with the GPON and the overlay video on the same network. One major new feature is the

inclusion of more security. In the original GPON, the threat model assumed that the upstream

2

1.2 Motivation

channel was physically secure, and this motivated a relatively weak security arrangement, which

was strengthened in later amendments to GPON. In XG-PON, the PON system is required to

support the option of strong mutual authentication, and to use the authentication to protect the

integrity of the PON management messages and the PON encryption keys. These enhancements

make it quite difficult for an attacker to masquerade as either an optical network unit (ONU)

or an optical line terminal (OLT), even if he has access to the PON fibres, and even if he can

precisely interleave his transmissions with the victim ONU [10].

To coexist with previous GPON standard, the downstream wavelength of operation of the

XG-PON is in 1575 - 1580 nm window whereas the upstream wavelength of operation of the

XG-PON is in the 1260 - 1280 nm window [2].

The XG-PON was defined as XG-PON1 when a asymmetrical bitrate of 10 Gbps in the

downstream and 2.5 Gbps in the upstream is used. In the case of a symmetrical bitrate, XG-

PON has a bitrate of downstream and upstream of 10 Gbps and it is called XG-PON2.

However when increasing the system rate to a 10 Gbps PON, some limitations arise, mainly

because the cost of the system has to be shared, leading to the use of low-cost equipment at the

user side. This self-imposed restriction has some effects in the performance of such equipment

which results in additional degradation of the system’s performance. This degradation comes

in many forms. However, in the case where the system’s transmission rate is increased, which

is the case that will be focused on, an effect that has very much influence on the system is the

Mode-Partition Noise (MPN) that will be explained later on. Also, the sensitivity of the receiver

itself has performance issues when there is such an increase in the data rate, and then motivating

the need for an evaluation of the receiver, which can be from a common PIN diode receiver to

an Avalanche photo-diode (APD) receiver.

The majority of service providers that employed GPON will skip XG-PON and jump to the next

standard. However, where the GPON is not deployed (i.e. greenfield) the use of the XG-PON

is strong option.

1.2 Motivation

The development of the 10 Gbps PON brings significant advantages to the access network.

The possibility of a higher bitrate per customer or more customers per PON are the obvious

enhancements. The increase of customers per PON leads to the need of a higher splitting ratio.

3

1. INTRODUCTION

The increase in the splitting ratio leads to a lower power level per customer for the same power

at the transmitter output. Thus, the study of the optical receiver employed gains significant

importance.

The higher bitrate may increase dispersion effects such as the MPN. The increase of the

MPN effect leads to an increase of the bit error rate and possibly cripple the link. The MPN

has a different impact on the system depending on the optical source. The nature of the MLM

laser makes it propitious to this type of noise. On the other hand, the SLM laser is in theory less

likely to be affected by this type of noise.

In this dissertation, the implementation of an APD receiver with MLM lasers or SLM

lasers as a solution for the reach increase of the XG-PON system is investigated. Moreover,

with the objective of enhancing the APD performance, an expression for the APD sensitivity

for a non-null extinction ratio is obtained. The degradation of the system performance induced

by the MPN is analysed.

1.3 Objectives and structure of the dissertation

The main objective of this work is to assess the extension of reach in a XG-PON system by

employing an APD receiver instead of a PIN receiver, in the presence of MPN.

This dissertation is composed by 6 chapters and 2 appendixes. The 6 chapters describe

and analyse the results achieved during the dissertation and the 2 appendixes are used to give

support to developed work.

In Chapter 1, the optical networks are presented, particularly, special attention is given to

the access networks. A brief history of the GPON is given, along with the legacy standards.

The XG-PON possible limitations are presented and the motivation for the realization of this

work is described.

In Chapter 2, the GPON standard fundamentals are presented, along with the description

of the basic architecture of a GPON system. The XG-PON system is introduced, and possible

solutions for receiver and transmitter are described.

In Chapter 3, the APD receiver is introduced. The signal at the input of the APD receiver

is characterized, a model for the APD is presented along with the characterization of the noise

after the APD receiver. An expression for the APD receiver sensitivity is proposed and its bene-

fits are evaluated. Also, it is proposed an expression for obtaining the optimum avalanche gain.

4

1.4 Main original contributions

In Chapter 4, the MPN is introduced and studied. The MPN in MLM lasers is studied, and

a model for the MPN in SLM lasers is proposed and evaluated. The effect of the MPN on the bit

error ratio is analysed through the study of the power penalty due to MPN, when using MLM

or SLM lasers.

In Chapter 5, the use of APD receivers in the XG-PON system is evaluated. The assess-

ment tests the possibility of the use of MLM lasers and SLM lasers. The reach extension of the

XG-PON system by using APD receivers instead of PIN is presented.

In Chapter 6, the final conclusions of this dissertation are outlined and proposals for future

work on this subject are made.

In Appendix A, the bit error rate model is described. The APD receiver expression for the

sensitivity is derived, along with the derivation of the APD optimum gain.

In Appendix B, the bit error rate in SLM lasers is described and analysed. A model for

obtaining the BER, based on an approximation, is proposed, and its validation is presented.

1.4 Main original contributions

In the analysis performed in this work, several original contributions were introduced relative

to other studies in the field. In the following, the list of the most important contributions of this

work are presented:

• Derivation of an expression for obtaining the APD sensitivity for non-null extinction ratio,

• Derivation of an expression for the APD optimum gain for non-null extinction ratio,

• Power penalty due to MPN when using MLM lasers based on APD sensitivity expression

for non-null extinction ratio,

• Model for obtaining BER in SLM lasers in the presence of MPN, considering a non-null

extinction ratio,

• Assessment of the XG-PON reach in the presence of MPN by using APDs.

5

1. INTRODUCTION

6

Chapter 2

Characterization of the XG-PON

In this chapter, it is presented the structure of the GPON system followed by the XG-PON sys-

tem. The definition of the two standards is presented, as the XG-PON is very much based on the

GPON. The features of the XG-PON are presented, along with the requirements to implement

it. It is given an overview of the receivers and transmitters that can be employed in the XG-PON

system.

2.1 Introduction to GPON

To better understand the XG-PON standard it is necessary to comprehend its predecessor, how

it all works, since the new standard is very much based on it. The architecture of the GPON

network is supported on a two-wavelength scheme, using WDM (wavelength division multi-

plexing), one for each stream direction, downstream (1490 nm) and upstream (1310 nm). There

is an optional wavelength (1550 nm) that can be used for transmitting analogue video, which

can be useful for distributing video in the site without the need of adding any other equipment;

in Fig. 2.1 there is an example of a GPON system. The maximum reach between an ONU and

an OLT is set to 60 km, with the limitation of distance between the closest ONU and the farthest

ONU not exceeding 20 km. Also it is specified that the split ratio cannot be more than 1:128,

which means that there is a theoretical limit to the number of users in a single PON equal to

128. In practical implementations of the standard the total number of users and the maximum

reach may be lower than the theoretical limits imposed by the recommendation, due to optical

power budget issues.

One of the first specifications of the G.984 recommendation is the physical-medium-

dependent (PMD) layer [2]. It covers the range of possible downstream/upstream rate combina-

7

2. CHARACTERIZATION OF THE XG-PON

OLT

ONT

ONT

ONT

1:N

WDM

RF Video

Downstream video: 1550 nm

Downstream: 1490 nm Upstream: 1310 nm

Central

Office

Figure 2.1: GPON system example.

tions along with the needed optical parameters for each of them. The preferred combination has

been the 2.488/1.244 Gbps, downstream and upstream respectively, which allowed for optimal

practice for the optical parameters, documented as an amendment to G.984.2. These parameters

are known as class B+ (allows for loss up to 28 dB) and applicable to a network whether it uses

the overlay video (optional third wavelength referred above) or not. The class B+ parameters

are not dependent on the receiver type, PIN or APD.

Part three of the recommendation G.984 is all about the Transmission Convergence layer

(GTC) [3], its main objective is to adapt the user data to the PMD layer. Though, it also provides

some basic management of the GPON network. There are two encapsulation methods allowed

by this specification, the GPON-encapsulation-method (GEM) and the asynchronous transfer

mode (ATM). However, virtually, only the former is used. The use of GEM permits: low over-

head adaptation to several protocols including Ethernet and time-division-multiplexing (TDM);

medium access control (MAC) function; the coordination of the interleaving of upstream trans-

missions from multiple ONUs. In the control plane, there is also the possibility of monitoring

the ONUs health and performance as well as the protocols and procedures for registering an

ONU in the GPON network. GEM offers the possibility to configure features on the transport

level such as the encryption, the bandwidth allocation and the forward error correction (FEC).

Looking into the GTC, there are two sub layers: the lower framing sub layer which defines the

GTC frame structure; the higher sub layer that deals with the TC adaptation through GEM.

In the lower layer, the overhead information is asymmetrical, meaning that the amount of

information is different when in upstream or downstream, however the framing structure does

8

2.1 Introduction to GPON

not vary with different GPON rates, only the size of the payload does.

The downstream GTC has a header containing: all overhead fields; the payload; a phys-

ical control block (PCBd) which includes the bandwidth map field, specifying the ONUs up-

stream transmission allocation; the physical layer operations, administration and maintenance

(PLOAM) field. The PLOAM field has the purpose of carrying a message-based protocol de-

signed for GTC and PMD layer management. It is important to mention that this downstream

frame is a 125us frame and transports an 8 kHz signal to provide a reference clock to the ONUs.

The upstream frame contains a sequence of ONU transmissions, previously dictated by the OLT.

Each of the transmissions frames has physical layer overhead field (PLOu) that includes a

preamble and a delimiter, both configurable by the OLT. The PLOu might have a dynamic band-

width report field, to help the dynamic bandwidth allocation mechanism, which carries traffic

queuing reports from the ONUs. It might also include a similar field to the downstream frame,

a PLOAM field. Both of the two referred fields are optional and only present upon request from

the OLT.

On the other hand, the higher layer is based on GEM, which defines a connection-oriented

encapsulation, independently of the protocol, with variable size packets. GEM has a virtual

connection unit with the name GEM port, where it contains the flows between logical and phys-

ical ports of an ONU. The port ID and the size of the frame are included in a 5-byte header

of the GEM frame. This frame can be fragmented which means a single packet can be split in

many GEM frames. The recommendation G.984.3 has appendices for the specification on the

transport of native TDM and Ethernet over GEM.

There is a unit for the upstream bandwidth allocation by the OLT named transmission

container (T-cont), configurable by the OLT. The most common configuration is based on one

T-cont per service class per ONU, or just a single T-cont per ONU. GEM ports are bundled onto

T-cont’s.

Bandwidth allocation can be done either in static method or dynamic (DBA). In GPON

there are two DBA defined methods: status-reporting DBA and non-status-reporting. The for-

mer is based on reports from the ONU via DBRu field in the upstream frame. The later consists

in monitoring T-cont utilization by the OLT. The control plane of the GTC layer is mainly

based on the PLOAM message protocol and some other overhead fields. The management op-

tions available include: PMD layer management - monitoring health of the physical layer and

generation of statistics and alarms when pertinent; GTC layer management related to the con-

9


figuration of GTC framing options, such as requesting PLOAM or DBRu, among other things;

The ONU activation defined in the GTC layer, is the process to activate an ONU on the OLT.

The optical power level of the ONU can be adjusted and it does the ranging procedure that

allows for setting the equalization delay by measuring the distance of the ONU to the OLT; En-

cryption management it is mandatory the use of Advanced Encryption Standard (AES) in the

downstream with a key for each ONU using an existing a well-defined process for the exchange

of key. Also, it can be applied per GEM port ID.

Finally, it was specified in G.984.4 the ONU management and control interface (OMCI).

The OMCI is a very important requirement in order to network operators to be able to have full

management of GPON systems, services and equipments, maintaining interoperability between

ONUs and OLTs from different vendors.

The OMCI is divided in two parts [4]: the ONU management base (MIB); the ONU man-

agement control channel protocol (OMCC), which exchanges the MIB information between the

OLT and the ONU. Inside the MIB, there is a group of managed entities, each one with its own

set of attributes. The creation of managed entities and their attributes is designated to either

the ONU or OLT. The modelling of the OMCI is very rich in content due to the vast variety

of interfaces and services that GPON ONUs may support. However, each MIB instance that

represents a specific ONU only contains a short subset of objects. Still, OMCI models phys-

ical aspects of the ONU like the various port types (i.e. plain old telephone service (POTS),

Ethernet, etc.), the equipment configuration and power. At the service layer, OMCI supports

high-speed internet (HSI) access recurring to quality of service (QoS) schemes and various flow

classifications, IPTV, voice over IP (VoIP), and so on. In each of these objects, OMCI supports

performance and fault management, as well as configuration. Additionally, OMCI standardizes

the housekeeping of the MIB itself and the software download for ONUs.

2.2 XG-PON

XG-PON was designed based on the existing GPON system, as a kind of an improvement

to the previous generation. It is defined by recommendation G.987.1. The XG-PON system

inherits: the TC layer principles; the dynamic bandwidth allocation; QoS and traffic manage-

ment; the remote operation of ONU through OMCI (redefined on G.988). This recommendation

also included improvements to the existing system, namely: enhanced power saving options;

10

2.2 XG-PON

synchronizing options enabling mobile back-hauling applications; upgrading the performance

monitoring; the optical distribution network (ODN); the security mechanisms [5].

On the PMD layer there is a difference on the downstream/upstream rate combination.

There are two standards, 10/2.5 Gbps (asymmetric) on XG-PON1 and 10/10 Gbps (symmetric)

on XG-PON2. The wavelengths chosen were 1575-1580 nm for the downstream and 1260-1280

nm for the upstream, allowing the coexistence with the previous generation and RF overlay

video [6].

GPON was class B+ (allows for loss up to 28 dB), and the coexistence of the two systems

implicates the use of a filter, which almost certainly will introduce additional loss. Also, some

deployed systems were designed with a bit more loss than required, for commercial reasons,

therefore two nominal budgets were introduced: nominal 1 that goes up to 29 dB; the nominal

2, for the over designed deployed systems, that goes up to 31 dB. In the GPON system an ex-

tended loss budget was developed that had two major features: 4 dB more loss than the nominal

budget, and ONU specifications that were unchanged from the nominal budget. After consid-

eration, the same desing features were reused in XG-PON leading to two extended budgets of

33 and 35 dB. There are no definitions on the receivers because both PIN and APD have their

specific advantages on the system. The ”decision” is left to be ruled by the market over the

years.

Although XG-PON transmission convergence (XGTC) layer is very much based on its

twin from GPON, it was more heavily structured with three distinct sub layers being defined:

the physical (PHY) adapting layer for handling issues related with the XG-PON physical layer;

the framing layer which is in charge of the PON TDMA system (the main work of the trans-

mission convergence layer); the client adaptation layer for dealing with the user signals and

carrying them over the XG-PON system.

The PHY adaptation sub-layer (PAS) deals with the low level coding in the TC frame in the

physical channel. One of the most important features is the use of FEC, required in both direc-

tions. Albeit, it can be turned off in the upstream provided that the link is good enough. There

are 24 bytes in each 125-microsecond frame reserved for a physical synchronization block in

the downstream (PSBd) destined to PAS operations such as: framing, by using the first 64 bits

with a fixed pattern, allowing the receiver to find the frame; super frame counter, occupying the

second 64 bits, providing a scrambler pre load and a much larger scale time reference; identifi-

cation of the PON, the third 64 bits are allocated for holding a value that is set by the OLT.

11


Traffic in the upstream direction in a PON is generally very few and as so, the upstream

is burst-transmission oriented, introducing some differences in the PSB for upstream (PSBu).

PSBu contains patterns for preamble and delimiting, with a payload that isn’t fixed size.

As for the second sub-layer, named framing sub-layer or FS, takes care of the TDMA part

of the PON, including activation and normal operation phases. XGTC has a header divided in

three parts: the first has a fix size, it contains the lengths of the other two parts and it is protected

with a header correction code (HEC); The second part is destined to carry a bandwidth map with

the several bandwidth allocations to the various ONUs on the PON; the last part contains the

PLOAM messages to the ONUs in the PON. The rest of the downstream XGTC frame is left

for the payload.

The bandwidth map concept is similarly to the GPON version, with some minor improve-

ments. As in GPON, each bandwidth allocation is for a sole ONU to transmit in upstream

and consecutive allocations can be concatenated together to improve efficiency. However, the

start-time and stop-time concept used in GPON is now dropped and replaced by a start-time

and a payload-length concept. This is an important difference since the payload-length is given

before the FEC overheads are added, facilitating the calculation of concatenated allocations

easier. Also the bandwidth allocation ID address has increased by 4 times its previous size,

allowing for wider split PONs. Moreover, there are customization possibilities since each allo-

cation specifies a burst profile. This profile includes the pattern and length of the delimiter, the

preamble and if FEC is active or not.

There are also improvements in the PLOAM messages inherited from GPON. It is now

possible to send more than one message per downstream frame, making the channel more re-

sponsive. The size of the message is increased to accommodate the known messages without

the fragmentation. Nevertheless, it were established limits to the maximum rate of each ONU

so that it will not overrun with messages. In the case of the upstream, there are two burst head-

ers: one that is fixed and contains the ONU-ID number plus the echo of the control information

from the allocation; the other is variable and carries the PLOAM message (if it exists). One

optional allocation header may exist for carrying the DBRu.

The client adaptation layer (CAS) formats the data packets to a suitable format for trans-

mission over the PON, called XG-PON encapsulation method (XGEM). Three aspects must be

dealt with: Individual flows of traffic (called ports in XG-PON) must be marked in order to be

accepted to by the right client. That is done using a 16-bit port ID, which is an increase by

12

2.2 XG-PON

16 times over the GPON correspondent address space, allowing wider split PONs; The fram-

ing header must occur at its periodic time, that can be difficult if a user packet is larger than

that boundary, so XGEM must take care of the fragmentation. XGEM allows fragmentation of

packets so that part can be transmitted in the current PON frame (or burst in the upstream) and

the other part at the next opportunity. GPON rules were enhanced so that very small fragments

are avoided and implementations are easier; Finally, XGEM must provide data privacy, which

is done by using a key index associated to every XGEM fragment. The index is obtained from

a previous negotiation between the OLT and the ONU. Key indexing permits a key switch-over,

in a well defined way, with no data loss at all, and coupled with the strong mutual authentication

makes XG-PON system very secure.

Management and service layers were directly inherited from GPON with a few modifi-

cations. The OMCI is the most complex interface to be standardized due to its variability,

evolution in time and requirement of interoperability. That is why the OMCI became an in-

dependent recommendation, allowing it to grow and adapt to all the new features and services

PONs were gaining. When the XG-PON OMCI definition was under debate, it has been decided

to make a generic recommendation just for the OMCI, recommendation G.988. This way, every

technology that wants to use it could just refer directly to it; this is the case of XG-PON as well

as GPON, which adopted recommendation G.988 after revision.

More recently, some changes had to be made to the original recommendations, and are

Video Downstream: 1550 nm

GPON Downstream: 1490 nm GPON Upstream: 1310 nm

1:N

WDM

RF Video

XGPON Upstream: 1270 nm XGPON Downstream: 1577 nm

XG-OLT

G-OLT

G-ONT

G-ONT XG-ONT

Central

Office

XG-ONT G-ONT

Figure 2.2: GPON and XG-PON coexistence example, assuming every ONU has a WDW filter.

called reach extensions. There are two types of reach limitations, the logical reach that is related

13


to the limits in the GTC (or XGTC) layer and the physical reach that is related with the PHY

limitations. Logically, the reach has limitations at the implementation level. The limitations are

imposed by the number of GTC (or XGTC) downstream frames that travel from the OLT to the

farthest ONU and how many BW maps the OLT has to store to properly map the corresponding

upstream frames. The logical reach of a GPON system is 60 km. On the other hand, the physical

reach is associated with the attenuation of the fibre, the loss budget and the split ratio. A GPON

system without reach extension and Class B+ transceiver may have a physical reach of 40 km

if the split ratio is 1:16. If split even further to 1:32 the reach decreases to half. It is easy to see

that the physical aspect is the bottleneck of the whole system since it imposes a shorter limit

than it should, ideally both limits should be equal. Focusing on the XG-PON system as opposed

to the GPON, the increase of rate produces a decrement in the receiver sensitivity [9], reducing

even more the physical reach. Introducing some gain in the system to achieve an optical budget

that allows the extension of reach may be a solution.

In Table 2.1, there is a summary of the GPON and XG-PON specifications and character-

istics.

System Down λ [nm] Up λ [nm] Down/Up [Gbps] Losses (Extended) [dB]

GPON 1490 1310 2.5/1.25 up to 28 (32)

XG-PON 1577 1270 10/2.5 or 10/10 up to 31 (35)

Table 2.1: Summary of GPON and XG-PON common characteristics.

2.3 Solutions for transmitter and receiver

The upgrade to a XG-PON system, with or without coexistence with the legacy system, requires

high-speed electronics to be used at both end-points of the network; at the ONU and, more

importantly, at the OLT, since it will need greater switching capacity. However, this increase

in the data rate arises several physical impairments at several sub-systems of the network: the

optical source, the optical receiver receiver and the optical transmission fibre. The deployment

of a new generation system by operators and service providers, and the acceptance of that

system by subscribers is largely dependent on the complexity and ultimately on the cost. It is

an inherent requirement to the development of PON systems that the cost should be as low as

14

2.3 Solutions for transmitter and receiver

it can be, maintaining the solution as simple as possible. Also, it is characteristic of this kind

of system that the majority of the network cost is due to the OLT and the ONUs. Thus, a brief

overview on the transmitter and receiver components is given.

2.3.1 Receiver

The employed receivers in the XG-PON endpoints (OLT and ONU) should be able work within

the XG-PON power budget. Thus, the receivers sensitivity is a key factor. Also, they must be

able to work in the wavelengths defined by XG-PON, shown on Table 2.1.

However, the ONU is very cost sensitive, and every effort to reduce its cost must be made.

The PIN type photodetectors become more attractive in comparison with APD types since,

generally, PIN receivers are less expensive. Nevertheless, APDs are far more sensitive than

PINs which leads to the use of less powerful OLT transmitter. In Section 2.2 there are defined

4 possible power budgets which are summarized on Table 2.2. In accordance with the specified

power budgets in Table 2.2, the possible options for the OLT-ONU pair are summarized on

Fig. 2.3. The information on Fig. 2.3 shows that the APD has the most advantages. The PIN

type receiver is only ”usable” in two budgets whereas the APD can be used with every budget

specified on Table 2.2. This work will focus on the APD as the chosen receiver.

Budget Designation Max Loss [dB]

Nominal 1 (N1) 29

Nominal 2 (N2) 31

Extended Nominal 1 (E1) 33

Extended Nominal 2 (E2) 35

Table 2.2: Summary of XG-GPON power budgets.

15


Figure 2.3: XG-PON possible OLT-ONU pairs, according to the XG-PON power budgets.

2.3.2 Transmitter

Since the ONU is very cost sensitive, the best approach would be to maintain the lower-end

components at the ONU, decreasing the deployment cost. With that in mind, the natural option

is to maintain the laser sources of the ONU, which represent a very large part of its cost, based

on Multi-Longitudinal Mode (MLM) lasers. The MLM lasers tend to be cheaper than the Single

Longitudinal Mode (SLM) lasers.

Semiconductor laser diodes exhibit two fundamental types of noise: (1) Quantum Shot

Noise, associated with the total power fluctuation, and (2) Mode-Partition Noise (MPN), car-

ried by each longitudinal mode. Provided that the laser uses direct modulation, the quantum

shot noise does not degrade the performance of the optical fibre digital system, unless the re-

flection from the fibre enhances this type of noise greatly. However, MPN has a key role in the

performance limitations of any optical system [11].

If we consider a Directly Modulated Laser (DML), either being a Distributed Feedback

(DFB) laser or a FP laser, severe fibre dispersion penalties will occur when using high data

rates, as is the case of the XG-PON system. This effect is particularly evident in the down-

stream transmission [12] as the upstream operates near the zero-dispersion wavelength, in the

1300 nm window. Thus, one could conclude that the transmitter used at the OLT is more criti-

16

2.4 Conclusion

cal than the ONU transmitter. So, a possible configuration would be to use a MLM laser as the

ONU transmitter and a SLM laser as the OLT transmitter. This work will have more focus on

the SLM lasers.

2.4 Conclusion

In this chapter, it was presented the GPON system and its features. The XG-PON sys-

tem, which is based on the GPON was then introduced along with changes introduced by the

new standard. The different layers of the XG-PON system were presented. Furthermore, the

possibilities for the XG-PON transmitter and receiver were reviewed.

17


18

Chapter 3

APD impact on the system performance

In this chapter, the APD receiver modelling and characterization are presented. A motivation for

the use of this sort of optical receiver is presented in section 3.1. The theoretical principles of

APD operation are briefly explained in section 3.2, followed by the characterization of the signal

and noise in sections 3.3 and 3.5, respectively. In section 3.6, a study of the APD sensitivity

is presented. In this study, it is derived an expression for the sensitivity that can be applied

to virtually any APD receiver, regardless of the on-off keying of the input signal or the APD

receiver parameters. Also, if the common approximations and assumptions are applied to the

new sensitivity expression, this new expression results in the commonly used APD receiver

sensitivity expression. Using this new expression for the receiver sensitivity, an equation for the

optimum avalanche gain, that leads to the maximum sensitivity, is also derived and validated.

3.1 Motivation for using an APD

As explained in chapter 2, any GPON system’s optical budget becomes more critical when

higher capacity and/or reach is needed, whether it is the new XG-PON or the legacy GPON.

Furthermore, the higher rate of 10 Gbps will cause the XG-PON to be strongly affected by the

degradation of the receiver sensitivity, provided the system conditions are similar to the legacy

system. The logical step to take is to introduce gain in the system, in order to minimize the

degradation effects. Also, it is desirable to enable the most affordable network provisioning

through minimization of the cost of network components. Preferably, changing the components

at the OLT allowing for the associated cost be shared by all ONUs in the network.

The gain introduction can be accomplished by using optical amplification in the terminal

elements of the network or replace the employed optical receiver PIN photo-diode by an APD

19

3. APD IMPACT ON THE SYSTEM PERFORMANCE

optical receiver, a photo-diode with gain.

However, the gain introduced by the APD is limited due to the classic noise and gain trade-

off [13]. Nevertheless, a considerable amount of effort has been done to determine the optimum

gain conditions in order to achieve the maximum receiver sensitivity [14].

3.2 Principles of APDs

The APD photo-diodes are a type of optical receiver that have the special property of providing

a built-in first stage of gain through the avalanche multiplication. They internally multiply the

primary photo-current before the following circuitry. The sensitivity increase happens since the

multiplication occurs before the photo-current encounter the thermal noise associated with the

receiver circuit. For the carrier multiplication to take place, the photo-generated carriers must

transverse a region where a very high electric field is present (as shown in Fig. 3.1). In this

high-field region, a photo-generated electron or hole can gain enough energy so that it ionizes

bound electrons in the valence band upon colliding with them. The newly created carriers are

also accelerated by the high electric field, thus gaining enough energy to cause further impact

ionization. This phenomenon is the avalanche effect [15].

Figure 3.1: Avalanche photo-diode reach-through schematic.

In order to achieve carrier multiplication with very little excess noise, it is commonly used

a reach-through structure (Fig. 3.1), which is composed by high-resistivity p-type material,

(material with a larger concentration of holes than electrons), deposited as an epitaxial layer on

a p` substrate [15]. A p-type diffusion is then made in the high-resistivity material, followed

by the construction of an n` layer, (layer of a material with a higher concentration of electron

20

3.3 Signal characterization

than holes). The nearly intrinsic π layer is simply an intrinsic material that inadvertently has

some p doping because of imperfect purification.

After entering the device through the p` region, light is absorbed in the π material, which

will collect the carriers that are photo-generated. This absorption will cause electron-holes

pair to appear, which will be separated due to the electric field in that region. The photo-

generated electrons will then move within this region, acquiring enough energy to generate a

new electron-hole pair. The energetic electron transfers part of its kinetic energy to another

electron in the valance band releasing it, leaving behind a hole. Thus, a single primary electron,

generated through absorption of a photon, creates many secondary electrons and holes, all of

which contribute to the photo-diode current. Similarly, the primary hole can also generate

secondary electron-hole pairs, contributing to the current. The generation rate is governed by

two parameters, α and β, the impact-ionization coefficients of electrons and holes, respectively.

These coefficients typically vary from one material to another.

It is called to the average number of electron-hole pairs created by carrier, per unit of

distance travelled, the ionization rate, represented by kA. The ionization rate is the ratio between

the holes and electrons impact-ionization coefficients. In practice, the APD performance is

better when the avalanche process is dominated by one charge ( α" β or β" α) [14].

3.3 Signal characterization

Let the value of the total multiplied output current be Imc and Ip the primary unmultiplied cur-

rent. Then, we may define the multiplication factor M for all carriers generated in the APD

as

M “Imc

Ip. (3.1)

The value of M is expressed as an average quantity due to the avalanche mechanism being a

statistical process; every diode carrier pair generated experiences a different multiplication.

Current gains differ from wavelength to wavelength. That dependence is attributed to

the mixed initiation of the avalanche process by holes and electrons when most of the light

is absorbed close to the detector surface, in the n`p region. This effect is more evident when

using short wavelengths where a major part of the optical power is absorbed close to the surface,

contrarily to what happens with longer wavelengths [15].

21


The optical receiver depend upon a minimum of current (Ip) to operate reliably, which is

the same to say that a minimum amount of power (pi) is needed for achieving that current. This

correlation is translated in expression 3.2, where Rλ corresponds to the unity gain responsivity.

pi “Ip

Rλ

(3.2)

So, the performance of an APD is also characterized by its responsivity, which is given by

expression 3.3 where η corresponds to the quantum efficiency, q is the electron charge, h is the

Planck’s constant and ν is the operating frequency of the optical signal.

RλAPD “ηqhν

M “ RλM (3.3)

Given the correlation between the minimum received power and the minimum current, detectors

with large responsivity are preferred since they minimize the optical power needed.

The received power is a combination of the power when the light source is off (bit 0),

commonly defined as pi,0, and the power when the light source is on (bit 1), known as pi,1.

In optical communications, for characterizing the signal it is also used a quantity named the

extinction ratio. This ratio, represented by r, is defined as quotient of the power of the bit 0 and

the power of the bit 1 as follows

r “pi,0

pi,1(3.4)

where 0 ď r ă 1. Nevertheless, ITU-T established that the maximum value of the extinction

ratio that can be used is r “ 0.152 [17]. The extinction ratio can also be represented as

Rext “pi,1

pi,0. (3.5)

Expression 3.5 is useful for representing the extinction ratio in dB, and the corresponding de-

fined limit is a minimum of 8.2 dB.

3.4 Receiver characterization

The optical receiver is responsible for converting the signals from the optical domain into the

electric domain and processing the resulting electric signal. There are optical receivers with

optical pre-amplification, which consists in using an optical amplifier before the optic-electric

22

3.4 Receiver characterization

conversion. The other kind of receivers are optical receivers without optical amplification, in

which the work focuses.

There are two key parameters related to the optical receiver: the sensibility, which is the

minimum average power required for achieving a determined bit error probability; the overload

parameter, which is the maximum input power that the receiver can withstand.

The optical receiver structure can be subdivided into two parts. One part specific of optical

receivers, where the conversion between an optical and electric signal is accomplished. The

other part is common to most receivers, and it is responsible for various functions such as

equalization and signal regeneration. On Fig. 3.2 it is shown the common structure for an

optical receiver.

Figure 3.2: Optical receiver structure.

The photo-detector converts the optical signal into an electrical signal through the photoelec-

tric effect. Since the generated electrical signal is generally very weak, it is necessary to add

a electric pre-amplifier for levelling the signal to be compatible with the following circuitry.

The noise power introduced by the pre-amplifier must be as low as possible since the optical

receiver performance is determined by the noised introduced by the pair photo-detector and

pre-amplifier [18]. In order to have a low noise power the pre-amplifier bandwidth must be

very limited. That limitation will introduce distortion in the input signal, which has codified

information. So, after the pre-amplification , the signal is regenerated, using the equalizer to

minimize the distortion effect caused by the pre-amplifier. After the signal is amplified using

electric amplifier that is associated with a automatic gain control (AGC). The AGC adjusts the

gain of the amplifier so that the output is approximately constant, regardless of the variations

23


in the input. The sampling and decision circuitry, which is synced by the clock signal from the

clock extraction circuitry, is then used to decode the signal.

The commonly used photo-detectors in optical fibre transmission systems are semiconduc-

tor photo-diodes. The most used types of photo-diodes are the PIN or the APD, in which this

work focuses.

3.5 Noise characterization

The main function of optical receivers is to convert the incident optical power pi into an elec-

trical current. In Eq. 3.2 it is assumed that the conversion is noise free, which is not true in

practice. There are two main noise mechanisms that lead to fluctuations in the current regard-

less of the incident optical signal having a constant power, the shot noise and the thermal noise.

In that way, Eq. 3.2 remains valid only if Ip is interpreted as the average current.

3.5.1 Thermal noise

At normal temperatures, higher than zero Kelvin, electrons will move randomly in any con-

ductor. This motion in a resistor manifests as a fluctuating current even in the absence of an

applied voltage. The load resistor RL in the front end of an optical receiver [19] will add these

fluctuations to the current generated by the photo-diode. Thus, this additional power component

is called the thermal noise, and it is represented by its variance σ2c given by

σ2c “ p4kBT{RLqFnBe,n (3.6)

where Fn represents the factor by which thermal noise is enhanced by the various resistors used

in pre and main amplifiers, Be,n is the effective noise bandwidth, the bandwidth of noise in hertz

over which the noise is considered, T is the temperature, and kB is the Boltzmann constant.

This noise is exactly the same in both PIN and APD, it does not depend on the photo-diode type

since it originates in the electrical components of the receiver.

3.5.2 Shot noise

The shot noise is a manifestation of the fact that an electrical current consists of a stream of

electrons generated at random times. As deducted in [19], the shot noise variance σ2s is defined

24

3.5 Noise characterization

by

σ2s “ 2qpIp` IdqBe,n (3.7)

where Id is the dark current, a current representing the constant response exhibited by a receiver

when not actively being exposed to light. However, in the case of the APD, the generation of

secondary electron-hole pairs at random times through the process of impact ionization, from

where the APD gain results are obtained, adds a contribution to the primary electron-hole pairs

associated shot noise. In fact, the multiplication factor is itself a random variable, being M the

average APD gain. Applying these considerations in Eq. 3.7 translates into [15]

σ2s “ 2qM2FApMqpRλ pi` IdqBe,n. (3.8)

In expression 3.8 FApMq is the excess noise factor of the APD, a factor that represents yet

another source of noise that describes the statistical noise inherent to the stochastic APD multi-

plication process. It is given by

FApMq “ kAM`p1´ kAqp2´1{Mq. (3.9)

The symbol kA in Eq. 3.9 represents the ionization coefficient ratio for the APD, which in

general increases with M and is in the range 0 ă kA ă 1. This value should be as small as

possible in order to achieve the best performance from an APD [16]. In the case of an PIN

receiver, M “ 1 which makes FApMq “ kA`1´ kA “ 1.

The simple plot of Eq. 3.9, as shown in Fig. 3.3, shows that the value of FApMq varies

between 2 and M, approximately. This confirms that lower values of kA lead to lower values of

excess noise factor. The mathematical result shown on Fig. 3.3 is explained physically by the

phenomenon quantified by the ionization rate kA. As stated in section 3.2, the ionization rate is

the ratio between the impact-ionization coefficients of holes and electrons, β and α, respectively.

Though, this dimensionless parameter is defined in two different ways, as kA “ β{α if α" β or

as kA “ α{β if β " α [14]. So, in either case, the greater the dominance of one charge over the

other in the avalanche process, the lower the ionization rate coefficient will be. Thus, based on

the statement in section 3.2 that dominance of one charge over the other is better in practice for

APD performance, lower values of ionization rate kA, lead to better APD performance.

25


M1 2 3 4 5 6 7 8 9 10

FA

(M)

1

2

3

4

5

6

7

8

9

10k

A = 0.01

kA = 0.5

kA = 0.99

Figure 3.3: Variation of the excess noise factor with avalanche gain for several values of kA.

3.6 APD receiver sensitivity

The nature of optic communications systems and the way they are deployed obliges the receiver

to be able to detect very weak optic signals. In some cases, the power levels may be near the

threshold of detection. The detection of very weak signals can only be done efficiently if the

optical receiver and the following circuitry are optimized to its limits.

The bit-error ratio (BER) is the performance criterion for digital systems. BER is defined

as the probability of incorrect identification of a received bit. Hence, the receiver sensitivity is

then defined as the minimum average received power required by the receiver to operate at a

certain BER. BER is given by

BER“12

erfcˆ

Q?

2

˙

«expp´Q2{2q

Q?

2π, Qą 3 (3.10)

where the parameter Q is the quality parameter. In appendix A.1, further detail on BER and the

quality parameter are presented. The parameter Q is given by

Q“I1´ I0

σ1`σ0(3.11)

where I1 and I0 are the average currents, and σ1 and σ0 are the square root of variances of bits 1

and 0, respectively. Since the BER is the used measure, when a target value is defined one must

be able to translate that value into a controllable parameter of the system. In the case of the

26

3.6 APD receiver sensitivity

optical receiver, this manageable parameter is the average incident optical power. In order to

relate the BER to the average incident power some analytical development must be performed.

In the denominator part of Eq. 3.11, there are the square root of variances of bits 0 and 1,

which are defined by

σ0 “

c

´

σ2s,0`σ2

c

¯

(3.12)

σ1 “

c

´

σ2s,1`σ2

c

¯

. (3.13)

From Eqs. 3.12 and 3.13, one can conclude that the square root variance of a given bit is

composed by the thermal noise contribution and the related bit shot noise contribution. Using

expression 3.8, the shot noise variance for bits 0 and 1 can be expressed in terms of their average

powers, pi,0 and pi,1, respectively, as follows

σ2s,0,1 “ 2qM2FApMqpRλ pi,0,1` IdqBe,n. (3.14)

where the average power pi,0 is then defined as

pi,0 “2pirp1` rq

, (3.15)

and pi,1 can be related to the total average power as

pi,1 “2pi

p1` rq. (3.16)

The numerator part of Eq. 3.11 is composed by the subtraction of the average currents of bit

1 and 0. Using Eqs. 3.2 and 3.3, the average currents of bit 1 and 0 can be related to their

corresponding powers, pi,1 and pi,0, respectively. Relating again the extinction ratio with the

average powers of bits 0 and 1, (see appendix A.2 for further details), an expression for the

subtraction of the currents in function of the total average incident power pi is obtained

I1´ I0 “MRλ

„

2pi

p1` rq´

2pirp1` rq

. (3.17)

Now, since all parts of Eq. 3.11 can be expressed in terms of pi, resolving the equation in

order to pi will lead to an expression where Q is a variable parameter in that expression. With

such an expression, one can define the target BER and obtain the corresponding Q value. Then,

27


replace that value on the pi expression and obtain the minimum average incident power that

complies to that BER target. This minimum power value is called the sensitivity.

Appendix A.3 details the equation analytical developments and considerations which re-

sulted in the sensitivity expression for an APD with non-null extinction ratio, given by

pi “Qpr`1q

MRλpr´1q2

„

QqFApMqMBe,npr`1q

`

b

p2qFApMqM2Be,nId`σ2cqpr´1q2` rp2QqFApMqMBe,nq2

.

(3.18)

The sensitivity pi depends on several optical receiver parameters, such as the receiver effective

bandwidth Be,n, the thermal noise variance σ2c , the responsivity Rλ. The dependency of the

receiver sensitivity on the avalanche gain is both direct, since expression 3.18 depends on M, and

indirect through the excess noise factor FA. This indicates that there will be a trade-off between

the gain value and the consequent introduced noise. The incident optical signal characteristics

dependency is represented by the extinction ratio r. Finally, as wanted, it depends on the Q

parameter, which is directly related with BER through Eq. 3.10.

The sensitivity expression 3.18 was derived for the APD receiver. However, it can be

applied to the PIN receiver by considering the PIN as an APD with unitary gain (M “ 1).

If one considers the simple case of a null extinction ratio (r “ 0), and also neglect the

contribution from the dark current (Id “ 0), the well known expression presented in [19] is

obtained

pi “QRλ

´

qFApMqQBe,n`σc

M

¯

. (3.19)

3.7 APD improvement over PIN

The improvement in the receiver sensitivity obtained by using an APD instead of a PIN can be

estimated by comparing the expression 3.18 and its version for a PIN diode (M “ 1). For a PIN,

the sensitivity expression 3.18 results in

piPIN “Qpr`1q

Rλpr´1q2

„

QqBe,npr`1q`b

p2qBe,nId`σ2cqpr´1q2` rp2QqBe,nq2

. (3.20)

28


The comparison between expressions 3.18 and 3.20 can be quantified by the ratio GAPD “

piPIN{pi, with pi being the sensitivity of the APD. This ratio represents how much additional

power a PIN receiver would need to match the performance obtained by the APD receiver. The

ratio is given by

GAPD “MQqBe,npr`1q`

a


QqBe,npr`1qc1à

p2qBe,nIdMc1`σ2cqpr´1q2` rp2QqBe,nc1q2

(3.21)

where

c1 “MFApMq. (3.22)

Expression 3.21 shows that the improvement of using an APD over a PIN diode is a function

of the avalanche gain M. Though, it is very hard to evaluate the improvement due to the large

number of parameters that influence it. To better understand how this improvement depends on

M, a plot of the GAPD (in logarithmic scale) versus the average avalanche gain M is shown in

Fig. 3.4. The parameters values were chosen based on an InGaAs APD, and the extinction ratio

used is the highest value permitted by the ITU-T specification [17]. The used values are shown

in Table 3.1. For further insight, 3 values of ionization rate kA were considered, given it has

influence on the excess noise factor FApMq.

Fig. 3.4 shows that the use of an APD can bring an improvement of several dB over the

Q r Rλ [A/W] Be,n [GHz] σ2c [A2] Id [nA]

7 0.152 1.0 8 p100ˆ10´9q2 3

Table 3.1: Set of typical values for sensitivity parameters

use of a PIN diode. As stated before, this improvement depends on the avalanche gain M of

the APD. Also, it can be seen that lower values of the ionization rate kA lead to a greater im-

provement, as it leads to lower values of excess noise factor. Thus, less noise introduced in the

system. In Fig. 3.4, it can also be seen that the improvement increases with the increase of M

till the optimum value of M is achieved. When that value is reached, the improvement is at its

maximum, since the sensitivity is at its maximum value. From that point on, the improvement

decreases and in certain circumstances, it is negative (i.e. the use of a PIN would be better).

Such odd behaviour can be explained by the effect of the excess noise factor.

29


Avalanche Gain (M)1 10 20 30 40 50 60

Sens

itivi

ty im

prov

emen

t (dB

)

-2

0

2

4

6

8

10

kA

= 0.1

kA

= 0.5

kA

= 0.99

Figure 3.4: Sensitivity improvement by using APD instead of a PIN diode.

Since the value of the avalanche gain is high, the noise associated with the avalanche gain

1 10 20 30 40 50 600

2

4

6

8

10

12

X: 22Y: 9.862

X: 25Y: 10.26

X: 28Y: 10.68

Avalanche Gain (M)

Sens

itivi

ty im

prov

emen

t (dB

)

r = 0.05r = 0.1r = 0.152

Figure 3.5: Sensitivity improvement by using APD instead of a PIN diode for three values of extinc-tion ratio for kA “ 0.1.

reaches a point where it becomes dominant in the receiver. This leads to a lower performance

when compared with the PIN, in which the excess noise due to the avalanche gain does not

exist.

30


The result shown in Fig. 3.4 allows for an analysis on how the ionization rate kA influences

the optimum gain of the APD. Again, the result confirms the conclusion of section 3.5.2 which

stated that lower values of ionization rate kA lead to better APD performance. Though, this

result also shows that lower values of ionization rate allow for a more stable performance, less

sensitive to minor changes in the optical receiver parameters, since the variation of the perfor-

mance around the optimum gain is smaller in lower values of ionization rate.

The result shown in Fig. 3.4 does not show the influence that the extinction ratio has on

1 10 20 30 40 50

1

2

3

4

5

6

7

8

9

X: 10Y: 7.402

X: 11Y: 7.727

X: 13Y: 8.071

Avalanche Gain (M)

Sens

itivi

ty im

prov

emen

t (dB

)

r = 0.05r = 0.1r = 0.152


the performance improvement. In order to show the extinction ratio influence, the improvement

plot was redone, with three extinction ratio values, r “ 0.05, r “ 0.1 and r “ 0.152, for each of

the ionization rates used in Fig. 3.4 . The plots are shown in figures 3.5, 3.6 and 3.7 , for values

of ionization rate kA “ 0.1, kA “ 0.5 and kA “ 1.0, respectively.

The extinction ratio decreases the APD improvement. The higher the extinction ratio, the

lower the improvement. Nevertheless, the extinction ratio influence is low when compared with

the ionization rate influence. The extinction ratio has impact on the improvement value, how-

ever it does not affect the ”stability” of that improvement. Thus, it can be concluded that when

designing an optical transmission system, the ionization rate is a much more critical parameter

than the extinction ratio.

31


1 10 20 30 40 50

1

2

3

4

5

6

7

8

X: 8Y: 6.57

X: 8Y: 6.268

X: 9Y: 6.884

Avalanche Gain (M)

Sens

itivi

ty im

prov

emen

t (dB

)r = 0.05r = 0.1r = 0.152


3.8 Analysis of sensitivity variation

The expression 3.18 for the sensitivity depends on many parameters. Thus, it becomes essential

a better understanding of how each one of those parameters influences the sensitivity level. A set

of typical values for all variable parameters, for the three most used materials in APD receivers,

are shown in Table 3.2. The considered materials were chosen for comparing purposes, as

shown in Fig. 3.8. Fig. 3.8 shows the dependence of the sensitivity on the APD gain M. It is

possible to see that there is an optimum gain M for which the maximum sensitivity is achieved.

Material Q r Rλ [A/W] Be,n [GHz] σ2c [A2] Id [nA] kA

Ge 7 0.152 0.73 8 p100ˆ10´9q2 100 0.9

InGaAs 7 0.152 1.0 8 p100ˆ10´9q2 3 0.45

Table 3.2: Set of typical values for APD receivers

From this point forward, the following analysis is based on the InGaAs APD, since it would

be a suitable choice for a XG-PON APD material. Thus, only InGaAs material parameters are

used.

32


Avalanche Gain (M)0 10 20 30 40 50 60 70 80 90 100

Sens

itivi

ty (

dBm

)

-28

-26

-24

-22

-20

-18

-16

GeInGaAs

Figure 3.8: Sensitivity variation with the avalanche gain for Ge and InGaAs APDs.

In expression 3.18, the responsivity parameter has a predictable influence on the sensitivity.

With the increase of the responsivity, the minimum amount of needed power decreases, which

means the sensitivity increases. Therefore, the performance of a system using APD optical

receivers is better when APDs with higher values of responsivity are employed. This mathe-

matical result can also be explained physically by understanding the meaning of responsivity.

The responsivity parameter in equation 3.18 represents the spectral response of the material.

The definition states that the spectral responsivity is the ratio of an optical detector’s electrical

output to its optical input, as a function of optical wavelength [17]. That means that higher

responsivity translates into lower input values for the same output value. Thus, it is implied that

a higher responsivity implicates a higher sensitivity of the optical receiver.

The effective noise bandwidth is a multiplying term that appears throughout the sensitivity

expression 3.18. It is expected that an increase of the Be,n will result in an increase of the power

pi, which means a decrease in the sensitivity. As depicted in section 3.5, both the thermal and

shot noise are proportional to the effective noise bandwidth, which means that the increase of

the effective noise bandwidth will increase the introduced noise in the system. Thus, the in-

crease of the effective noise bandwidth reduces the sensitivity. A plot of the sensitivity using all

parameters from Table 3.2 except for the Be,n is shown in Fig. 3.9, demonstrating the effective

noise bandwidth impact on the sensitivity. The plot was made by varying the Be,n between 10%

and 100% of the bit ratio of 10 Gbps (XG-PON bitrate) for plotting purposes, to better show

the influence of the effective noise bandwidth. Although, since the first Nyquist criterion states

33


that the bandwidth should be at least 50% of the binary rate in order to avoid inter-symbolic

interference (ISI), usually the effective noise bandwidth is between B{2 and B, with B being

the system transmission bit rate. Several values of avalanche gain were considered, to study the

influence of the effective noise bandwidth as the gain increases.

The expected impact of the effective noise bandwidth on the sensitivity is verified. How-

1 2 3 4 5 6 7 8 9 10−34

−33

−32

−31

−30

−29

−28

−27

−26

−25

−24

Be,n

(GHz)

Sen

sitiv

ity (

dBm

)

M = 5

M = 10

M = 20

M = 40

Figure 3.9: Sensitivity variation with the effective noise bandwidth value for kA “ 0.45 and r “0.152.

ever, the effect is greater at higher values of avalanche gain M. For lower values of M, the

difference can be within a range of 1 dB whereas for higher values the variation may be around

8 dB, for the parameters used. Therefore, the effective noise bandwidth Be,n should be as low

as possible so that its influence may be minimized. Though, since the effective noise bandwidth

is depend of the binary rate, there is a trade-off between speed and bandwidth.

Similarly to the effective noise bandwidth, the excess noise factor FApMq is also a mul-

tiplying factor. However, its value depends on two parameters, the ionization rate kA and the

avalanche gain M. So, in order to study the excess noise factor impact on the sensitivity, ex-

pression 3.18 was plotted using the parameters from Table 3.2, except for the ionization rate kA,

and it is shown in Fig. 3.10 .

The effect on the sensitivity caused by the excess noise factor FApMq is similar to the

effect of the effective noise bandwidth Be,n. The sensitivity decreases with the increase of the

excess noise factor FApMq. Also, the excess noise factor FApMq effect has greater impact when

the avalanche gain is higher. Still, the excess noise factor increases with the increase of the

34


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−36

−34

−32

−30

−28

−26

−24

kA

Sen

sitiv

ity (

dBm

)

M = 5

M = 10

M = 20

M = 40

Figure 3.10: Sensitivity variation with the ionization coefficient ratio value for Be,n “ 8 GHz andr “ 0.152.

ionization rate kA, consequently, the sensitivity will decrease with the increase of the ionization

rate. To obtain better performance one can either decrease the ionization rate, use an optimum

avalanche gain or both.

In Fig. 3.8, it was concluded that the avalanche gain M increases the sensitivity till the op-

timum avalanche gain M is achieved and, after the optimum gain M the sensitivity will decrease

with the increase of the gain. The excess noise factor is responsible in part for that decrease

in the sensitivity. For higher values of ionization rate the excess noise factor will have a more

preponderant impact. Thus, the conclusion in section 3.7 over the ”stability” of the sensitivity,

when subjected to minor variations in its value, is now reinforced, justified by the lower values

of excess noise factor.

Lastly, there is the input signal characterization parameter, the extinction ratio r. This

parameter influence can be examined by plotting the sensitivity expression 3.18 using all pa-

rameters from Table 3.2 except the extinction ratio. The plot is shown in Fig. 3.11. It was used

the extinction ratio R “ 1{r, converted to dB, starting at about 8 dB (r “ 0.152), which is the

minimum value considered to be valid by ITU [17]. In the plot shown in Fig. 3.11, the values

exceeding 30 dB have no physical meaning, so it was the limit value.

The effect of the extinction ratio increase (or decrease in the case of r) is more perceptible

for lower levels rather than with higher levels of R. The phenomenon present on the plot, with

the avalanche gain M “ 5 and M “ 20 leading to similar results, is explained by the optimum

35


10 12 14 16 18 20 22 24 26 28 30−29

−28

−27

−26

−25

−24

−23

−22

−21

R (dB)

Sen

sitiv

ity (

dBm

)

M = 5

M = 10

M = 20

M = 40

Figure 3.11: Sensitivity dependence on the extinction ratio value Be,n “ 8 GHz and kA “ 0.45.

gain, which is near M “ 10. Thus, the performance increases till that optimum avalanche gain

and decreases afterwards, which explains the similar curves in Fig. 3.11 .

The extinction ratio being lower means physically that the levels of the bit 0 and 1 powers

are far from each other and consequently, far from the medium value. Increasing the distance

between bit signal levels leads to a bigger margin for noise, since the level of noise added to

one bit power level in order to equalize the other level increases. Thus, the odds of identifying

the correct bit improve. Therefore, in terms of APD performance, it is best that the extinction

ratio r is as close to 0 as possible.

3.9 Optimum avalanche gain

Throughout the analysis in section 3.8 it was stated that there is an optimum gain for an APD.

The avalanche gain is important since, in the case of the excess noise factor, the avalanche gain

has a direct influence in the level of noise introduced on the system. Thus, in this section the

avalanche gain will be scrutinised. Its analysis is a bit more complicated since it has direct

(and indirect through the excess noise factor FApMq) influence on various parts of the sensitivity

expression 3.18. In appendix A.5 it was derived an approximated expression for the optimum

36

3.9 Optimum avalanche gain

avalanche gain, and it is given by

MOptimum “

c

Be,nQqkApr`1q”

a

σ2cpr´1q2`pkApr`1q´ r´1qBe,nQq

ı

Be,nQqkApr`1q. (3.23)

Expression 3.23 is merely an analytical re-engineered expression based on an approximation

expression for the sensitivity (mode details in appendix A.5), given by

pi,apx “Qpr`1q

MRλpr´1q2

„

Qpr`1qqFApMqMBe,n`

b

σ2cpr´1q2

. (3.24)

For validating the use of Eq. 3.23 as a valid approximation for computing the optimum

5 10 15 20 25 30 35 40

−30

−29

−28

−27

−26

−25

−24

−23

−22

X: 13Y: −29.32

X: 13Y: −29.49

Avalanche Gain (M)

dBm

pipi,apx

Figure 3.12: Sensitivity versus sensitivity approximation, with extinction ratio r “ 0.05.

avalanche gain MOptimum, expression 3.24 should be compared against expression 3.18. Also,

the approximation performed should be valid within the valid extinction ratio range (i.e. 0 ď

r ď 0.152). In Fig. 3.12 , 3.13 and 3.14 , is shown the plot of expressions 3.24 and 3.18 for the

extinction ratio values of r “ 0.05,r “ 0.1 and r “ 0.152, respectively. The APD considered

was a InGaAs APD, with parameters in Table 3.2.

In Figs. 3.12 , 3.13 and 3.14 it can be seen that near the optimum gain region, the ap-

proximate expression gives a value with an error of less than 0.5 dB. The error increases with

the increase of the extinction ratio, which is explained by the approximation, where the ne-

37


5 10 15 20 25 30 35 40

−29

−28

−27

−26

−25

−24

−23

−22

−21

X: 12Y: −28.54

X: 12Y: −28.8

Avalanche Gain (M)

dBm

pipi,apx


5 10 15 20 25 30 35

−29

−28

−27

−26

−25

−24

−23

−22

−21

X: 11Y: −27.74

X: 11Y: −28.07

Avalanche Gain (M)

dBm

pipi,apx


glected contribution (mode details in appendix A.5) corresponds to bit 0 contribution. Despite

the increase in the error, within the target extinction ratio domain ( 0 ď r ď 0.152), the error is

below 0.5 dB. Therefore, it can be concluded that expression 3.24 is a good approximation and

consequently, Eq. 3.23 can be used to compute the optimum avalanche gain.

38

3.10 Conclusion

3.10 Conclusion

In chapter 3, the fundamentals of APD were given. Two points that have impact in the APD

performance: the characterization of the signal and the noise, were described. These points

were discussed using mathematical expressions.

An expression for the sensitivity for an arbitrary extinction ratio was obtained. Thus, it

is possible to compute the sensitivity value given any set of APD parameters, independently

of the input signal characteristics (i.e the extinction ratio value). Furthermore, an analysis of

that expression was presented, leading to a better understanding of how each of its parameters

influence the sensitivity. It was found that the extinction ratio has great impact on the APD per-

formance, and the APD performance is better for lower extinction ratios. Also, it was presented

numerically the improvement of an APD over a normal PIN receiver.

Lastly, an approximated expression for the optimum avalanche gain that leads to the high-

est sensitivity value was achieved. Through that expression the avalanche gain value can be

obtained for any given set of APD parameters, leading to the best sensitivity with an error

below 0.5 dB.

39


40

Chapter 4

MPN impact on the system performance

In this chapter, the transmitter impairments due to the Mode Partition Noise (MPN) are dis-

cussed. Since MPN is a phenomenon associated with optical laser sources, an overview of the

basic concepts of a semiconductor laser is presented in section 4.1. The introductory section is

followed by the characterization and modelling of the MPN in section 4.2. In this section, it is

given the approach for Multi-Longitudinal Mode (MLM) lasers and Single Longitudinal Mode

(SLM) lasers. Finally, it is presented in sections 4.6 and 4.7 the impact of the MPN effect on the

performance of MLM lasers and SLM lasers, respectively. For both types of lasers, the perfor-

mance impact is measured in a form of a power penalty, which will be useful when designing

the optical communication system.

4.1 Basic concepts of semiconductor lasers

The main objective of the optical transmitter is to convert an electrical input signal into the

corresponding optical signal so that it can be launched in the optical fibre. The optical trans-

mitters major component is the optical source, which are either light-emitting diodes (LEDs) or

semiconductor lasers. Each of them offer different advantages. The use of semiconductor lasers

became practical after 1970 [22], when continuous operation at room temperature of such lasers

became possible.

All materials absorb light rather than emit it, under normal conditions. Though, if the

photon energy hν of the incident light is about the same as the energy difference between two

levels ( Eg“E2É1 ) the photon is absorbed by the atom. The atom ends up in the excited state.

Once in the excited state, eventually the atom will return to its normal ”ground” state and, when

41

4. MPN IMPACT ON THE SYSTEM PERFORMANCE

that occurs, light is emitted. This light emission can happen through two fundamental processes

known as spontaneous emission and stimulated emission [19]. The spontaneous emission refers

to when photons are emitted in random directions with no phase relationship among them. The

stimulated emission, by contrast, is when the process is initiated by an existing photon and, has

the remarkable feature that the emitted photons match the origin photon. The emitted photons

mimic the origin photon not only in energy and frequency, but also in other very pertinent char-

acteristics, such as the direction of propagation.

Semiconductor lasers are a subset of lasers. All of them emit light through the stimulated

emission process and, thus, are said to emit coherent light. On the other hand, LEDs emit light

through spontaneous emission and, therefore, are an incoherent light source [19].

Semiconductor lasers are pumped electrically using a p´ n junction, as shown in [19].

When the injected carrier density in the active-layer exceeds a certain value, population inver-

sion phenomenon (more electrons on the conduction band than in the valence band) happens

[19]. The active layer will then exhibit optical gain by a factor of exppgLlayerq, where g is the

gain coefficient and Llayer the active-layer length. Nevertheless, this optical gain by itself is

not enough for laser operation. The other necessary ingredient is optical feedback, which turns

any amplifier into an oscillator. Most lasers feedback is provided by placing the gain medium

inside a Fabry-Perot (FP) cavity formed by two mirrors. However, semiconductors lasers do not

require external mirrors as the two cleaved facets can mimic the mirrors behaviour, simulating

a FP cavity. Despite the FP cavity formed by the two cleaved facets having a significant loss,

the gain in a semiconductor laser is high enough so that those losses can be tolerated.

According to [19], there is a phase condition that lasers must match

νm “mc

2nLlayer(4.1)

where m is a positive integer and n is the optical mode index. Thus, the laser frequency ν must

match one of the frequencies in the set νm. These frequencies correspond to the longitudi-

nal modes and are determined by the optical length nLlayer. The spacing between longitudinal

modes is constant and is given by [19]

∆νL “c

2ngLlayer(4.2)

where ng corresponds to the group index.

42

4.2 Characterization of MPN

The gain spectrum is wide enough so that many of the longitudinal modes of the FP cavity

experience gain simultaneously [19]. The mode that is close to the gain peak becomes the dom-

inant mode and the other modes, under ideal conditions, would not reach threshold since their

gain would be less than the main mode. However, due to the extremely small frequency differ-

ence that exists between modes, in practice, some of the neighbouring nodes on each side of the

main mode can carry a significant portion of the laser power. Since each mode propagates in-

side the fibre at slightly different speed due to group-velocity dispersion, the multi-mode nature

of the laser often limits the bit rate of light-wave system. This impairment could be overcome,

improving the performance of the optical system, by designing lasers that oscillate in a single

longitudinal mode, the SLM lasers.

The basic idea for a semiconductor laser that emits light predominantly in a single lon-

gitudinal mode is to design the laser in such a way that the losses are different for different

longitudinal modes of the cavity, as opposing to what happens in FP lasers, whose losses are

independent of the mode. The longitudinal mode that has the smallest cavity loss will achieve

threshold first and, therefore, becomes the dominant mode, while the neighbouring modes have

higher losses. In this case, the power portion carried by these side modes is usually a small

fraction of the total emitted power. For a SLM laser, the side mode suppression is often charac-

terized by the side-mode suppression ratio (SMSR), defined as

SMSR“Pmm

Psm(4.3)

where Pmm is the average power of the main mode and Psm is the average power of the most

dominant side mode. SMSR should be above 30 dB for a good SLM laser [19], which is the

minimum side-mode suppression ratio recommended by ITU-T [20].

4.2 Characterization of MPN

The MPN is related with the laser source. The lasing modes compete at slightly different wave-

lengths leading to fluctuation in the relative portion of the modal powers, though the total output

power remains essentially constant [23]. The optical power fluctuation at different longitudinal-

mode wavelengths interacting with the chromatic dispersion of the fibre results in a random

profile of the output pulse intensity. The random nature of source power distribution among

43


longitudinal-mode wavelengths incurs in amplitude and phase noise, simultaneously [23].

Figure 4.1: Random power spectrum at different time instants t1, t2, for illustrating the partitionnoise.

This effect on the optical pulse propagation appears in both single-mode and multi-mode

fibres, as it depends on the interaction between the chromatic dispersion characteristic of the

fibre and the optical source. It can substantially degrade the performance of transmission sys-

tems, operating at high-speeds. In a dispersion-less fibre link, even if the transmission is running

at very high speed, the laser mode partition noise will have no effect. All modes will propa-

gate along the fibre synchronously, avoiding the inter-symbol interference and the consequent

degradation of the signal at the receiver end.

In 1982, Ogawa and Vodhanel stated that the MPN produces an effect of a pulse-delay

fluctuation, and the error rate cannot be reduced by increasing the received signal power [24].

This is an important statement, as it implies that the MPN cannot be mitigated by simply in-

creasing the received signal power. In fact, once the MPN becomes the dominant contribution,

no more improvements can be made in the transmission system [25].

4.3 MPN modeling

In MLM lasers, lasing mode competition causes the mode fluctuations observed during the

injected current transient. Lasing mode competition is the phenomenon in which different res-

onator modes experience laser amplification in the same gain medium. That effect leads to

cross-saturation effects and random occurrences of another phenomenon, known as random

mode partitioning, which is a time-varying laser spectrum.

44

4.3 MPN modeling

For the purposes of the analysis, let us formulate the following assumptions: (a) the total

power carried by each optical pulse emitted by the semiconductor laser is constant; (b) at the end

of the fibre link, the optical waveform detected will be distorted through chromatic dispersion

characteristic of the optical fibre medium; (c) spontaneous emission contribution within each

longitudinal mode is neglected, only stimulated emission is taken into account when assessing

the optical power of each emitted longitudinal mode.

Assuming the laser source emitted N longitudinal modes, and identifying by ci the random

variable representing the relative power of the ith mode, the total relative power is equal to 1, as

given byNÿ

i“1

ci “ 1 (4.4)

where the variable ci is given by the ratio between the power of the ith mode pimode and the total

power ptotal , defined by

ci ”pimode

ptotal. (4.5)

At the end of the fibre link, the total optical pulse shape detected can be expressed by the

sum of each of its partial pulse responses yiptq “ ypt,λiq. Each of them corresponds to each

of the emitted longitudinal modes, being λi the wavelength of the ith mode. Normally, the

chromatic dispersion of the fibre affects every mode differently, so it can be assumed that

ypt,λiq “ ypt,λ jq, i “ j. Therefore, the total pulse response assumes the meaning of a random

process rptq and is given by

rptq “Nÿ

i“1

ypt,λiqci. (4.6)

At the sampling time t “ t0, the measured fluctuation in the detected optical pulse is dependent

on the composition of the N waveforms for every available power distribution. Using expression

4.6, the total detected optical pulse amplitude r0 is also a random variable

r0 ” rpt0q “Nÿ

i“1

ypt0,λiqci ”

Nÿ

i“1

y0pλiqci. (4.7)

The fluctuation of power in the random variable r0 assumes the meaning of mode partition noise

[25]. Using expression 4.7, the variance of MPN is given by[25]

σ2MPN

∆“ xr2

0y´xr0y2. (4.8)

45


where xvy stands for the average value of the variable v.

4.3.1 Mode-partition coefficient

To evaluate σMPN , recurring to expression 4.8, expression 4.4 must be examined. The measured

time-average power spectrum Psmpλiq shows the average value of the mode power of each mode

at its λi wavelength

xciy “ Psmpλiq

“

ż

. . .

ż

ciPsmpc1,c2, . . . ,cNq ¨dc1dc2 . . . ,dcN

(4.9)

where Psmpc1,c2, . . . ,cNq is the joint probability distribution function of c1,c2, . . . ,cN . Evaluat-

ing σMPN through expression 4.8 requires that Psmpc1,c2, . . . ,cNq is known, which is generally

not the case. In [27], Ogawa has introduced the concept of mode partition coefficient kMPN

defined by

k2MPN “ 1´α“

xc2i y´xciy

2

xciy´xciy2(4.10)

and it is assumed that xcic jy “ αxciyxc jy for all modes with i “ j where α is a constant. This

assumption translates in practice to assume that every longitudinal mode consists of the stim-

ulated emission, and not spontaneous emission. This assumption is the most critical of this

model, as it may not always be true for semiconductor lasers. However, it allows to evaluate

σMPN without the knowledge of Psmpc1,c2, . . . ,cNq, by using kMPN .

Another form of presentation [25] of kMPN is given by

k2MPN “

Nř

i“1

Nř

j“i`1

`

xciyxc jy´xcic jy˘

Nř

i“1

Nř

j“i`1xciyxc jy

(4.11)

In this form, it can be seen that there are two limiting cases: i) if laser modes are statistically

independent

xcic jy “ xciyxc jy ñ kMPN “ 0 (4.12)

46

4.3 MPN modeling

ii) if laser modes are mutually exclusive

xcic jy “ 0ñ kMPN “ 1. (4.13)

Despite having an expression, the numerical value of kMPN is relatively uncertain and

may depend on a large number of parameters. Nevertheless, a widely used value suggested by

experimental measurements is kMPN “ 0.5 [27].

4.3.2 Mode-partition noise

The variance of MPN, recurring to expressions 4.6 and 4.8, is given by [25]

σ2MPNpkMPNq “ k2

MPN

$

&

%

Nÿ

i“1

y0pλiqxciy´

«

Nÿ

i“1

y0pλiqxciy

ff2,

.

-

(4.14)

It is assumed in expression 4.14 that, after equalization at the receiver, the received signal is of

the form

y0pλiq “ ypλi, t0q “ cosrπBpt0`∆τiqs (4.15)

where B is the bit rate and

∆τi “ LDpλi´λ0q (4.16)

corresponds to the relative delay of the ith partition mode with respect to the central partition

mode λ0, during propagation along a fibre with chromatic dispersion parameter Dλ and length

L. Since the decision circuit samples the signal at times t0 “ N{B, where N is an integer,

expression 4.15 is actually

ypλi, t0q “ cosrπB∆τis. (4.17)

Assuming that xciy can be described by a continuous Gaussian distribution [27], xciy is given

by

xciy “ Psmpλiq “1

σ?

2πexp

„

´pλi´λ0q

2

2σ2

. (4.18)

where σ is the laser r.m.s. spectral width.

Furthermore, considerably simplifying the calculation, the discrete sum in expression 4.14

can be replaced by an integral. Those simplifications allows for calculating the numerical value

47


of σMPN . The standard deviation of MPN, σMPN , is then given by

σMPN “kMPN?

2

“

1´ expp´β2q‰

(4.19)

where

β“ πBDλLσ (4.20)

is a dimensionless parameter. The obtained expression 4.19 for the MPN shows that σMPN is

directly proportional to the mode-partition coefficient kMPN defined by expression 4.10.

4.4 MPN in MLM lasers

The MPN effect in MLM lasers can be estimated by adding a noise term to the total noise at

the receiver. This additional noise term is added to the receiver noise so that Q is determined by

[27]1

Q2 “

„ˆ

1` r1´ r

˙

σ0`σ1

2MRλP

2

`

”

σMPN

1

ı2(4.21)

where σ0 and σ1 are the square root of the variances of bits 0 and 1, respectively, P is the average

received signal power at the receiver, r is the extinction ratio, M is the average avalanche gain

of the receiver and Rλ is the responsivity. The power penalty induced by MPN is related to the

received power that is necessary to maintain a constant SNR [26]. Let us consider Qn given by

Qn “

d

Q2

1´Q2σ2MPN

(4.22)

where Q is determined using expression 3.10. Then, expression 4.21 becomes similar to Eq.

A.15 from the appendix A used to derive the sensitivity expresion 3.18. Thus, the power in

the presence of the MPN, Pn, can be obtained by using expression 3.18 using Qn instead of Q.

Morever, the power in absence of MPN, P0, can be obtained using 3.18 using Q. Therefore the

power penalty (in decibels) is given by

αMPN “ 10log10

ˆ

Pn

P0

˙

. (4.23)

The MPN has a critical importance when designing an optical transmission system. For ex-

ample, if the desired BER is 10´12 which corresponds approximately to Q “ 7, the maximum

48

4.5 MPN in SLM lasers

value of σMPN for the power penalty to be under 1 dB is σMPN « 0.0867 .


There is a major difference between multi-mode and (nearly) single mode lasers, which is the

statistics that characterize the mode-partition fluctuations. In MLM lasers, the side modes are

typically above threshold and, therefore, are well described by a Gaussian probability density

function whereas, in a SLM laser, side modes are typically below threshold. SLM side modes

follow an exponential distribution given by [19]

ppPsmq “1

Psmexp

„

´Psm

Psm

, (4.24)

where Psm is the average value of the power of the side mode Psm.

For better understanding the effect of side mode fluctuations on system performance, an

ideal receiver is considered (no dark current nor thermal noise and 100% quantum efficiency

[19]).

Let ∆τ “ DL∆λ be the relative delay between the main mode and the side mode, where

∆λ is the mode spacing. Let us assume that ∆τ ą 1{B which implies that BLD∆λ ą 1. This is

the same to say that it is assumed the relative delay is long enough that the side mode does not

reach the bit slot in time. Let the decision threshold be at Pmm{2, being Pmm the average power

of the main mode. There will be an error if the transmitted bit is 0 and the receiver detects a

value above the threshold or if the transmitted bit is 1 and the receiver detects a power below the

threshold. Also, it is assumed that the total power remains constant, i.e. the two modes are anti-

correlated so that when main mode power drops below threshold, side mode power will exceed

it. Since 0 and 1 have can be considered equally probable, BER is defined by (see detailed BER

in appendix A.1) [25]

BER“ż `8

Pmm{2ppPsmq dPsm “ exp

ˆ

´Pmm

2Psm

˙

“ expˆ

´SMSR

2

˙

(4.25)

where SMSR corresponds to the side-mode suppression ratio defined in equation 4.3. If a BER

of the 10´12 is considered, leads to a minimum SMSR « 17.4 dB.

The general expression for BER when a non-ideal receiver is considered is more compli-

cated than expression 4.25.

49


An approach to obtain BER is to consider the side-mode current as a noise current. That ap-

proach is detailed in Appendix B.1. However, it does not account for the fluctuations of the

main mode current.

The main mode current i0,1ptq, for bit 0 or 1, can be considered a random variable with an

associated statistical distribution. If the two mode laser is considered, the total current after the

optical receiver is then given by

iT0,1ptq “ i0,1ptq` isptq (4.26)

where isptq corresponds to the current after the optical receiver resulting from the side-mode.

It is known [31] that the total laser current iT0,1ptq follows a Gaussian distribution. However,

we may define the total current as iT0,1ptq “ IT0,1 ` δiT0,1ptq, where only δiT0,1ptq is a random

variable and corresponds to the fluctuations of the total current. The variable IT0,1 corresponds

to the total average current for bit 0 or 1. Hence, the probability density function for δiT0,1ptq is

given by

pδT0,1pxq “1

σT0,1

?2π

exp

˜

´x2

2σ2T0,1

¸

. (4.27)

Considering the probability of bit 0 and 1 to be equal, the BER is given by

BER“ PpiT0ptq` iG0ptq ą IDqPp0q`PpiT1ptq` iG1ptq ă IDqPp1q. (4.28)

Substituting iT0,1ptq, the BER is given by

BER“12rPpδiT0ptq` iG0ptq ą ID´ IT0 “ ID0q`PpδiT1ptq` iG1ptq ă ID´ IT1 “ ID1qs (4.29)

where iG0,1ptq corresponds to the Gaussian noise current for bits 0 or 1, and ID the decision

threshold. The resulting BER expression (detailed in appendix B.2) is given by

BER“14

»

—

—

–

erfc

¨

˚

˚

˝

ID´ I0Ím

SMSRc

2´

σ2T0`σ2

0

¯

˛

‹

‹

‚

` erfc

¨

˚

˚

˝

I1Ìm

SMSR ´ IDc

2´

σ2T1`σ2

1

¯

˛

‹

‹

‚

fi

ffi

ffi

fl

. (4.30)

50


The value of ID that minimizes the BER (details in Appendix B.2) is obtained from:

ID “

b

σ2T1`σ2

1

´

I0Ìm

SMSR

¯

`

b

σ2T0`σ2

0

´

I1Ìm

SMSR

¯

b

σ2T0`σ2

0`b

σ2T1`σ2

1

(4.31)

Thus, BER is given by

BER“12

erfcˆ

Q?

2

˙

(4.32)

where Q is given by

Q“I1´ I0

b

σ2T0`σ2

0`b

σ2T1`σ2

1

. (4.33)

The variance of bit 0, σ20, and the variance of bit 1, σ2

1, are given by expressions 3.12 and 3.13,

respectively. The variance of the total current after the optical receiver for bit i, σ2Ti

, is given by

(details in Appendix B.2)

σ2Ti“ σ

2mm,i´σ

2sm,i (4.34)

where the variance of the laser intensity noise σ2mmi

is given by

σ2mmi

“ RλMPirl (4.35)

where Pi is the power of bit i and the parameter rl is a measure of the noise level of the incident

optical signal. The parameter rl is considered as the inverse of the SNR of the light emitted by

the transmitter [19]. Typically, the transmitter SNR is better than 20 dB and rl ă 0.01 [19]. The

side-mode noise variance is given by

σ2smi“

ˆ

RλMPi

SMSR

˙2

(4.36)

It has been considered that bit 0 and bit 1 are equally likely to occur. Based on that assumption,

the average current of the main mode Im may be defined as

Im “12

I0`12

I1. (4.37)

51


4.6 Penalty for using a MLM laser

When a MLM laser is employed, the power penalty may be calculated using equations 4.19

and 4.23. It was indicated in section 4.3.1 that a common used value for the mode-partition

coefficient is kMPN “ 0.5 [27] and in [29] it is suggested that kMPN is within the 0.6-0.8 range.

So, for the purpose of the analysis, several values of kMPN were considered. In Fig. 4.2, it can

be seen how the penalty is influenced by the dispersion parameter β, for a value of Q “ 7. For

- parameter0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Pow

er p

enal

ty (

dB)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

kMPN

= 1.0

0.8

0.6

0.4

0.2

Figure 4.2: Power penalty when using a MLM laser as a function of β parameter, for various valuesof kMPN for Q“ 7.

a BER level of 10´12 (Q = 7), the power penalty of the MPN in a MLM laser increases greatly

with β. For high values of kMPN , the power penalty may become infinite (i.e. the defined BER

of 10´12 is not achievable) for β values above a certain point. For experimental values of kMPN ,

in the previous specified range of 0.6-0.8, the power penalty becomes infinite for values of β

above 0.5. Therefore, considering the XG-PON bitrate of 10 Gbps and using expression 4.20,

the distance is limited to Lă 1{p10ˆ109πDσq. Considering D“ 17 ps/(nm/km) and σ“ 2nm

[29], the distance is limited to Lă 0.94 km. In Fig. 4.3 ,it is represented the power penalty for a

BER level of 10´3 (Q = 3). It can be seen that, for a higher BER, the mode-partition coefficient

kMPN has less influence on the power penalty.

When designing an optical system, the β parameter is not the used metric. In fact, light-

52

4.7 Penalty for using a SLM laser

- parameter0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Pow

er p

enal

ty (

dB)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

kMPN

= 1.0

0.8

0.6

0.40.2

Figure 4.3: Power penalty when using a MLM laser as a function of β parameter, for various valuesof kMPN for Q“ 3.

wave systems are usually designed such that [29] BDLσ ă 0.2, which as per Eq. 4.20 means

that β{πă 0.2ô βă 0.2π« 0.63. In this case, the power penalty can be as low as a negligible

0.5 dB or infinite, depending on the value of kMPN . To render the penalty to negligible values

(ď 0.5 dB), independently of the kMPN value, one must design a system where β ď 0.336,

approximately. Such imposition means that BDLσ ă 0.1. Therefore, if the usual measure of

[29] BDLσă 0.2 is cut down by one half, the MLM MPN power penalty is not noticeable. The

σ and D are fixed parameters, intrinsic to the laser and fibre used, respectively. Thus, there is a

trade-off between transmission speed B and covered distance L.

4.7 Penalty for using a SLM laser

In SLM lasers, the evaluation of the power penalty induced by MPN is dependent on the value

of Q, defined in expression 4.33. Since BER is given by Eq. 4.32, the BER value is set by the

value of Q. Expression 4.33 can be analytically manipulated to be expressed in terms of power

value. The power penalty is then given by

∆PMPN “ 10log10

ˆ

P0

PMPN

˙

(4.38)

53


where PMPN is the power in the presence of MPN and P0 is the power in the absence of MPN

(i.e. SMSR “ `8). Unless otherwise stated, the parameter values on Table 4.1 were used to

obtain the numerical results.

Considering a BER target of 10´12, it is shown in Fig. 4.4 the relation between the side-mode

Q r Rλ [A/W] Be,n [GHz] σ2c [A2] Id [nA] kA M rl

7 0.1 0.5 8 p100ˆ10´9q2 2.5 0.5 1 0.01

Table 4.1: Parameters used for obtaining numeric results.

suppression ratio and the increase of the power at the receiver, for the values of M “ 1 and

M “ 10.

SMSR (dB)0 5 10 15 20 25 30 35 40

Incr

ease

of r

ecei

ved

pow

er (d

B)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

M = 10

M = 1

BER = 10-12

Figure 4.4: Relation between the increased power at the receiver and the side-mode suppressionratio, considering a reference BER of 10´12 and r “ 0.1, for M “ 1 and M “ 10.

If we consider a greater avalanche gain (M “ 10), as shown in Fig. 4.4, it can be seen that

the increase in the avalanche gain decreases the needed power. However, the influence of the

avalanche gain is low and thus, the decrease in the power penalty is low. Also, it can be seen

54

4.8 Conclusion

that, for values of mode-suppression ratio SMSR ě 30 dB, which is the minimum required by

ITU-T, the power penalty is negligible.

The extinction ratio r is an important parameter of the optical transmission system and has

SMSR (dB)0 5 10 15 20 25 30 35 40

Incr

ease

of r

ecei

ved

pow

er (d

B)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

r = 0.152

r = 0.1

r = 0.01

BER = 10-12

Figure 4.5: Relation between the increased power at the receiver and the side-mode suppressionratio, considering a reference BER of 10´12 and M “ 10, for r “ 0.01, r “ 0.1 and r “ 0.152.

great influence on the optical receiver performance, as seen on Chapter 3. A smaller extinction

ratio increases the power level difference between power level of bits 0 and 1. Therefore,

the expected behaviour is that the power penalty decreases with lower extinction ratios and

increases with higher extinction ratios. In Fig. 4.5, it is shown the power penalty using the

extinction ratio values of r “ 0.01, r “ 0.1 and r “ 0.152 (maximum allowed by ITU-T), for

an avalanche gain of M “ 10. The power penalty decreases with the extinction ratio decrease.

However, the power penalty variation is low and is negligible for values of SMSR used in

practice (SMSR ě 30 dB).

4.8 Conclusion

In this chapter, the MPN was presented and the importance of the MPN was explained. A

theoretical introduction to the laser sources and the MPN was given.

55


The MPN due to MLM lasers was discussed. The study of the power penalty study caused

by MPN, when MLM lasers are employed, concluded that, at the XG-PON bitrate of 10 Gbps,

there is a great limitation on the achievable distance.

It was discussed a model for obtaining the BER in presence of MPN with SLM lasers. The

presented model takes into account the fluctuations on the main mode and the noise introduced

by the side mode of the SLM laser. The model is based on the Gaussian approximation for the

total current after the receiver [31] and the model that describes the SLM laser of [32]. However,

the obtained BER expression 4.30 is simpler than BER expression from [32].

The power penalty for SLM lasers, which is obtained using BER expression 4.30, was

discussed. The avalanche gain of the receiver and the extinction ratio have low influence on

the power penalty since the side-mode suppression ratio imposed by ITU-T is SMSR ě 30 dB.

Thus, the effect of MPN is equal for a PIN receiver or an APD receiver. The power penalty is

negligible for values of SMSR above 30 dB.

56

Chapter 5

Assessment of XG-PON reach improvement

In this chapter, it is discussed the improvement of the XG-PON reach when using APDs instead

of a PIN receiver, in the presence of MPN. The assessment is accomplished by considering all

possible combinations of lasers and receivers types at the OLT and ONU.

5.1 Link budget of the XG-PON system

The operation of a XG-PON system requires that the emitted power at the OLT (or ONU)

reaches the ONU (or OLT) at a level that the optical receiver can correctly identify the bits sent,

with a desired BER. As it was seen in Chapter 3, the needed power level at the receiver, Pi,

depends on multiple parameters concerning the type of optical receiver employed as well as

system parameters. A system parameter, defined in the design of the XG-PON system is the

BER. In the following sections, the assessment of XG-PON reach considers a BER target of

10´12, which is the typical case when Forward Error Correction (FEC) is not employed. The

case of FEC employment is also evaluated, which corresponds to a target BER of 10´3. The

receiver sensitivity Pi is also dependent on the employed extinction ratio, which concerns the

optical source. An extinction ratio of r “ 0.1 is considered.

In the XG-PON system, the typical optical budget follows the equation given by [18]

Pr ě PeÁlink ą Pi (5.1)

where Pr corresponds to the power at the receiver input, Pe is the power emitted at the transmitter

output and Alink is the total attenuation. Typically, it is considered a system margin Ms given by

57

5. ASSESSMENT OF XG-PON REACH IMPROVEMENT

[18]

Ms |dB “ PeÁlink´ Pi´∆PipDλLq |max (5.2)

where ∆PipDλLq |max is the maximum path penalty due to dispersion in the XG-PON system

transmission, and is set to 2 dB. The system margin Ms should cover a safety margin (due to

unexpected losses) Msa f “ 3 dB and other margins due to ageing and variations in the environ-

ment and temperature. A minimum of Ms “ 6 dB is required for the system margin [18].

The path penalty due to the dispersion is given by

∆PipDλLq |dB“ ∆PipDλLq |LdB `∆PipDλLq |MdB `∆PipDλLq |MPNdB (5.3)

where ∆PipDλLq |MdB is the power penalty associated with the modulated bandwidth, ∆PipDλLq |LdB

is the power penalty associated with the source linewidth and ∆PipDλLq |MPNdB is the power

penalty associated with the MPN.

The attenuation due to the transmission and passive components, Alink, is given by

Alink “ NcAc`NsAs`α f L`NspAsp (5.4)

where Nc is the number of connectors used and Ac is the connector attenuation, Ns is the number

of splices and As is the splices attenuation, Nsp is the number of splitters and Asp is the splitter

attenuation, α is the fibre attenuation per km and L is the distance in km. Thus, the optical

power budget is then given by

Pe ě Pi`MsÀlink`∆PipDλLq |max (5.5)

By using expressions 5.5 and 5.4, it is obtained the maximum distance L that can be accom-

plished. The maximum distance is given by

LďPe´Pi´MsŃcAcŃsAsŃspAsp´∆PipDλLq |max

α f. (5.6)

Unless otherwise stated, the parameters used for the XG-PON system are shown in Tables 5.1,

5.2 and 5.3.

Throughout the following section, the APD receiver is compared against a PIN receiver in

order to assess the reach extension when using an APD. Unless otherwise stated, the parameters

58

5.1 Link budget of the XG-PON system

kMPN As [dB] Ac [dB] Ms [dB] r BER Down λ0 [nm] Up λ0 [nm]

0.5 0.06 0.3 6 0.1 10´3 / 10´12 1577 1270

Table 5.1: Typical parameters of XG-PON system used for obtaining numerical results.

λ0 [nm] Dλ [ps/(nm.km)] α [dB/km]

1577 18.41 0.23

1270 -3.68 0.45

Table 5.2: Typical G.652 fibre parameters used for obtaining numerical results [34].

Split Ratio As [dB]

1:2 3.63

1:4 7.22

1:8 10.72

1:16 13.95

1:32 17.30

1:64 20.78

1:128 24.19

Table 5.3: PON split ratios and corresponding losses [35].

used for the receiver are shown in Table 5.4. The receiver sensitivity in dBm Pi“ 10log10` pi

1mW

˘

is computed from expression 4.33 derived in Chapter 4. The PIN receiver is considered by

setting the avalanche gain M “ 1. The downstream FEC code is RS(248, 216) whereas the

upstream FEC code is RS(248, 232) [8]. The increase of effective noise bandwidth, Be,n, with

the FEC code ratio is given by

Be,nFEC “ Be,nnk. (5.7)

where n is the block length and n is the message length for the FEC code RS(n,k). Taking into

Rλ [A/W] Be,n [GHz] σ2c [A2] Id [nA] kA M

0.5 8 p100ˆ10´9q2 2.5 0.5 10

Table 5.4: Receiver parameters used for obtaining numerical results.

account the values shown in Table 5.4 and the FEC codes for each direction, the sensitivity

59


values for a PIN receiver and an APD receiver, with FEC and without FEC, were computed and

are shown in Table 5.5. Following the information in Fig. 2.3, we assume that the transmitting

Q BER FEC Code Pi APD [dBm] Pi PIN [dBm]

With FEC Downstream 3 10´3 RS(248, 216) -30.16 -21.33

With FEC Upstream 3 10´3 RS(248, 232) -30.08 -21.32

Without FEC 7 10´12 - -25.31 -17.61

Table 5.5: Sensitivities used for obtaining numerical results.

powers for the OLT and ONU lasers are those in Table 5.6. The values chosen correspond to

the lowest power emitted when a PIN receiver is used.

Tx OLT [dBm] Tx ONU [dBm]

10.5 2

Table 5.6: Emmiting powers for the optical sources of OLT and ONU using MLM and SLM lasers.

The XG-PON system can be constituted by only one splitter or several, if cascading is

applied (e.g. using a splitter of 1:2 and one of 1:4 instead of applying a splitter of 1:8). For

simplicity, only one splitter is considered. Thus, let us consider two connectors, one at the OLT

and one at ONU, two splices in the splitter and a splice every 1.36 km. The XG-PON has two

maximum distances 20 km and 40 km [7], the following sections use those maximum distances.

5.2 Improvement using MLM lasers

5.2.1 Downstream

Consider the use of a MLM laser as an optical source for the OLT. In the downstream direction

the chromatic dispersion parameter is Dλ “ 18.41 ps/(nm.km), for the operating wavelength

λ0 “ 1577 nm, and the bitrate is 10 Gbps. Assuming a spectral half-width of σ “ 2 nm [29]

for the MLM laser and using expression 4.23, the power penalty for L “ 20 km due to MPN is

∆PipDλLq |MPN“ 8 for both the scenario without FEC and the scenario with FEC. Therefore,

the MLM laser cannot be used as the optical source at the OLT.

60

5.2 Improvement using MLM lasers

5.2.2 Upstream

Consider the use of a MLM laser as an optical source for the ONT. In the upstream direction

the chromatic dispersion parameter is Dλ “ ´3.68 ps/(nm.km) obtained from [34], for the op-

erating wavelength λ0 “ 1270 nm. The bitrate is 10 Gbps if the XG-PON is designed to have a

symmetrical bitrate or 2.5 Gbps if the XG-PON has an asymmetrical bitrate. Assuming a spec-

tral half-width of σ “ 2 nm [29] for the MLM laser, a bitrate of 10 Gbps and using expression

4.23, the power penalty for L“ 20 km due to MPN is ∆PipDλLq |MPN“8 for both the scenario

without FEC and the scenario with FEC. For the case of where a 2.5 Gbps bitrate is used, the

power penalty for L “ 20 km due to MPN is ∆PipDλLq |MPN“8 for the scenario without FEC

and ∆PipDλLq |MPN“ 1.91ă 2 dB for the scenario with FEC.

Let us consider the case where FEC is employed and evaluate the penalty associated with

the source linewidth ∆PipDλLq |LdB and the penalty associated with the modulated signal band-

width ∆PipDλLq |MdB. The power penalty ∆PipDλLq |MdB is given by [19]

∆PipDλLq |MdB“ 5log10`

p1´8αcβ2LB2q

2`p8β2LBq2

˘

(5.8)

where αc is the chirp parameter and β2 is given by [19]

β2 “´Dλλ2

02πc

. (5.9)

In the upstream, if conventional bulk lasers are considered, the chirp parameter is αc « 6 [18].

Therefore, the power penalty associated with the modulated signal bandwidth is ∆PipDλLq |MdB“

0.08 dB.

The power penalty ∆PipDλLq |LdB is given by [19]

∆PipDλLq |LdB“´5log10“

1´p4BDλLσλ,Lq2‰ (5.10)

where σλ,L is the r.m.s. spectral width and it is given by [19]

σλ,L “∆λL

2.35(5.11)

where ∆λL is the laser linewidth. For MLM lasers, the linewidth is typically 1 ď ∆λL ď 5 nm

[18]. Therefore, assuming ∆λL “ 2 nm, the power penalty associated with the source linewidth

61


∆PipDλLq |LdB“ 1.08 dB. Consequently, the total dispersion penalty ∆PipDλLq |dBě 2 dB . There-

fore, the MLM laser cannot be used in either the OLT or the ONU.

5.3 Improvement using SLM lasers

5.3.1 Downstream

In Chapter 4, it was concluded that the SLM mode-suppression ratio should have a high value

in order to achieve lower power penalties. Unless otherwise stated, the mode-suppression ratio

considered is SMSR “ 30 dB. The penalties consider the bitrate of 10 Gbps and a distance of

L “ 20 km. Using expression 4.33 and expression 4.38, the power penalty is ∆PipDλLq |MPNdB «

0.075 dB for the PIN and ∆PipDλLq |MPNdB « 0.027 dB for the APD. The obtained values for the

MPN penalty are similar whether FEC is employed or not.

Let us evaluate the penalty associated with the source linewidth ∆PipDλLq |LdB and the

penalty associated with the modulated signal bandwidth ∆PipDλLq |MdB . The typical linewidth

(in Hz units) of the SLM laser is 1 ď ∆υ ď 100 MHz [19]. If we consider ∆υ “ 50 MHz,

∆λ “λ2

0∆υ

c « 8.3ˆ 10´13 m. Thus, the power penalty associated with the source linewidth is

∆PipDλLq |LdB“ 0 dB. In the XG-PON system, the lasers at the OLT are externally modulated

lasers (EML) [37], which means that the chirp parameter is αc« 0 [19]. Thus, the power penalty

associated with the modulated signal bandwidth is ∆PipDλLq |MdB“ 0.31 dB. Therefore, the total

dispersion penalty ∆PipDλLq |dBď 2 dB.

If we consider the distance of L “ 40 km, ∆PipDλLq |MdB“ 1.03 dB and ∆PipDλLq |LdB“ 0

dB. Therefore, the total dispersion penalty ∆PipDλLq |dBď 2 dB. Thus, the dispersion does not

limit the link of the XG-PON in the downstream direction.

The maximum distance imposed by the optical budget is given by

LB ď10.5´Pi´6´p2ˆ0.3q´pNsAsq´p1Âspq´∆PipDλLq |max

0.23. (5.12)

Using expression 5.2 for obtaining the system margin, it is shown in Table 5.7 the distances

imposed by the optical power budget for both the PIN and the APD receiver for every splitting

ratio and system margin for a distance of L “ 20 km as a function of the splitter ratio, when

FEC is not employed.

When FEC is not employed, the PIN receiver is limited by the optical budget to a splitting

62


Splitter ratio PIN max LB [km] APD max LB [km] Ms PIN [dB] Ms APD [dB]

1:2 64.70 98.17 16.28 23.98

1:4 49.09 82.57 12.69 20.39

1:8 33.87 69.00 9.19 16.89

1:16 19.82 54.96 5.96 13.66

1:32 5.26 40.39 2.61 10.31

1:64 -9.87 25.26 -0.87 6.83

1:128 -24.70 10.43 -4.28 3.42

Table 5.7: Maximum distance imposed by the power budget and system margin for L “ 20 km,for both PIN and APD receivers as function of the splitter ratio without FEC, in the downstreamdirection.

ratio of 1:16, whereas the APD receiver supports splitting ratios up to 1:64. The commonly

used splitting ratios are between 1:8 and 1:64 [19]. Thus, the APD covers the use of all com-

mon splitting ratios for L “ 20 km and up to 1:32 for L “ 40 km. In the case where FEC is

employed, the results are in Table 5.8.

The use of a PIN at the ONU allows a splitting ratio up to 1:32, and is limited by the


1:2 80.82 118.91 19.99 28.75

1:4 65.21 103.30 16.40 25.16

1:8 50.00 88.43 12.90 21.66

1:16 35.96 74.04 9.67 18.43

1:32 21.39 59.47 6.32 15.08

1:64 6.26 44.35 2.84 11.60

1:128 -8.57 29.52 -0.57 8.19

Table 5.8: Maximum distance imposed by the power budget and system margin for L “ 20 km, forboth PIN and APD receivers as function of the splitter ratio using FEC, in the downstream direction.

optical budget for higher splitting ratios. On the other hand, the APD receiver supports a split-

ting ratio up to 1:128. If we consider a distance of L“ 40 km, the PIN receiver only supports a

splitting ratio up to 1:8 whereas the APD receiver supports up to 1:64 splitting ratio. Again, the

use of an APD covers the use of all common splitting ratios at both L“ 20 km and L“ 40 km.

63


5.3.2 Upstream

In the upstream scenario, for both 2.5 Gbps and 10 Gbps bitrate, the power penalty due to MPN

is the same used in section 5.3.1.

Let us evaluate the penalty associated with the source linewidth ∆PipDλLq |LdB and the

penalty associated with the modulated signal bandwidth ∆PipDλLq |MdB . If we consider ∆υ“ 50

MHz as the linewidth of the SLM laser, ∆λ “λ2

0∆υ

c « 5.4ˆ 10´13 m. Consider the distance

L “ 20 km, the power penalty associated with the source linewidth is ∆PipDλLq |LdB“ 0 dB

for both 10 Gbps and 2.5 Gbps bitrate. In the XG-PON system, the lasers at the ONU are

directly modulated lasers (DML) [37], which means that the chirp parameter is αc « 6 [18].

The power penalty associated with the modulated signal bandwidth is ∆PipDλLq |MdB“ 0.12 dB

for 2.5 Gbps and ∆PipDλLq |MdB“ 1.67 dB for 10 Gbps. Therefore, the total dispersion penalty

∆PipDλLq |dBď 2 dB.

If we consider the distance of L“ 40 km, ∆PipDλLq |MdB“ 2.87 dB and ∆PipDλLq |LdB“ 0 dB

for a bitrate of 10 Gbps. The XG-PON system is dispersion limited for the distance L“ 40 km at

a 10 Gbps bitrate. However, for a 2.5 Gbps bitrate, ∆PipDλLq |MdB“ 0.24 dB and ∆PipDλLq |LdB“ 0

dB. Therefore, the total dispersion penalty ∆PipDλLq |dBď 2 dB for an upstream bitrate of 2.5

Gbps.

Consider the case where FEC is not employed, using expression 5.2 for obtaining the

system margin, Ms, it is shown in Table 5.9 the distances imposed by the optical power budget

for both the PIN and the APD receiver for every splitting ratio and system margin for a distance

of L“ 20 km as a function of the splitter ratio.

When the PIN receiver is employed at the OLT, the distance L“ 20 km is not achievable.


1:2 14.18 31.29 3.38 11.08

1:4 6.20 23.31 -0.21 7.49

1:8 -1.58 15.53 -3.71 3.99

1:16 -8.76 8.36 -6.94 0.76

1:32 -16.20 0.91 -10.29 -2.59

1:64 -23.93 -6.82 -13.77 -6.07

1:128 -31.51 -14.04 -17.18 -9.48

Table 5.9: Maximum distance imposed by the power budget and system margin for L “ 20 km, forboth PIN and APD receivers as function of the splitter ratio without FEC, in the upstream direction.

64


Under the conditions tested and using an APD receiver, the XG-PON system is limited to a

splitting ratio of 1:4 when FEC is not employed for a distance of L“ 20 km. The results for the

case when FEC is employed are shown in Table 5.10.

The use of a PIN at the OLT limits the XG-PON system to 1:2 splitting ratio. On the


1:2 22.42 40.89 7.09 15.85

1:4 14.44 33.91 3.50 12.26

1:8 6.67 26.13 -0.01 8.76

1:16 -0.51 18.96 -3.23 5.53

1:32 -7.96 11.51 -6.58 2.18

1:64 -15.69 3.78 -10.06 -1.30

1:128 -23.27 -3.80 -13.47 -4.71

Table 5.10: Maximum distance imposed by the power budget and system margin for L“ 20 km, forboth PIN and APD receivers as function of the splitter ratio using FEC, in the upstream direction.

other hand, the APD receiver supports a splitting ratio up to 1:8. The distance of L “ 40 km is

only achievable if an APD receiver is employed and a splitting ratio of 1:2 is used. To use the

common splitting ratios FEC is mandatory, the OLT receiver needs to be an APD and, in the

case of the splitting ratios 1:32 and 1:64, the emitted power at the ONU has to be increased.

It is shown in Table 5.11 a summary of the results obtained. Under the conditions studied,

the XG-PON system is limited by the optical budget in the upstream direction, which leads to

a maximum distance of L “ 20 km, for the commonly used splitting ratios. Also, the splitting

ratio of 1:128 is not achievable. The obtained result is consistent with other results [38] and

[39].

PIN APDFEC Upstream Downstream Upstream Downstream

No - 1:16 1:4 1:64

Yes 1:2 1:32 1:8 1:128

Table 5.11: Summary of usable splitting ratios for L“ 20 km.

65


5.4 Conclusion

In this chapter, it was presented an assessment of the XG-PON reach improvement by using an

APD receiver as opposed to a PIN receiver. A set of typical parameters for all XG-PON system

components was presented and the analysis developed was based on those parameters. It was

analysed the use of MLM lasers in downstream and upstream directions. The MLM lasers can-

not be employed due to the high dispersion suffered by the signal emitted by an MLM laser.

Also, it was analysed the use of the SLM lasers in downstream and upstream directions.

In the downstream direction, the use of the APD instead of a PIN at the ONU allows an im-

provement of reach and higher splitting ratio. Furthermore, the use of an APD receiver allows

the use of the common splitting ratios, between 1:8 and 1:64, for distances of L “ 20 km and

L“ 40 km, in the downstream direction. However, under the conditions studied, to achieve the

common splitting ratios in the upstream direction, the use of an APD receiver at the OLT is

mandatory, FEC needs to be employed and the emitting power of the ONU transmitter has to

be increased. Moreover, under the conditions studied, the splitting ratio of 1:128 and a distance

of L“ 40 km was not achieved due to limitations in the upstream direction.

66

Chapter 6

Conclusion and future work

In this chapter, the final conclusions of the work developed in this dissertation are presented, as

well as suggestions for future work.

6.1 Final conclusions

In this dissertation, the assessment of the reach improvement by using APD receivers in the

presence of MPN was performed. Both MLM and SLM laser sources were considered. There-

fore, the optimization of the APD receiver and the model used to characterize the BER in the

presence of MPN gains special relevance in this work. The APD sensitivity was analysed and

an expression for the APD sensitivity for non-null extinction ratio was proposed. In addition, a

model for BER in SLM lasers when MPN is present was proposed and analysed.

In chapter 2, the fundamentals of the XG-PON were given. The possibilities for receivers

and transmitters were reviewed.

In chapter 3, the fundamentals of APD were given, with focus on the factors that influence

the APD performance. An expression for numerically obtain the sensitivity, for an arbitrary ex-

tinction ratio, was derived. Furthermore, an analysis of that expression was presented, leading

to a better understanding of how each of its parameters influence the sensitivity. It was found

that the extinction ratio has great impact on the APD performance, and the APD performance is

better for lower extinction ratios. Also, it was numerically presented how much an APD could

be an improvement over a normal PIN receiver.

An approximated expression for the optimum avalanche gain that leads to the highest sen-

sitivity value was achieved. Through that expression, the avalanche gain value can be obtained

for any given set of APD parameters, leading to the best sensitivity with an error below 0.5 dB.

67

6. CONCLUSION AND FUTURE WORK

In chapter 4, the MPN was presented and the importance of the MPN was explained. A

theoretical introduction to the laser sources and the MPN was given. The MPN due to MLM

lasers was discussed. The study of the power penalty study caused by MPN, when MLM lasers

are employed, concluded that, at the XG-PON bitrate of 10 Gbps, there is a great limitation on

the achievable distance.

It was discussed a model for obtaining the BER in presence of MPN with SLM lasers. The

presented model takes into account the fluctuations on the main mode and the noise introduced

by the side mode of the SLM laser. The model is based on the Gaussian approximation for the

total current at the receiver output [31] and the model that describes the SLM laser of [32]. The

obtained BER expression 4.30 is simpler than BER expression from [32] and is valid for values

of SMSR ě 30 dB.

The power penalty due to MPN for SLM lasers, which is obtained using BER expression

4.30, was discussed. The avalanche gain of the receiver and the extinction ratio have low influ-

ence on the power penalty since the side-mode suppression ratio imposed by ITU-T is SMSR

ě 30 dB. The power penalty is negligible for values of SMSR above 30 dB.

In chapter 5, it was presented an assessment of the improvement of the XG-PON reach by

using an APD receiver as opposed to a PIN receiver. A set of typical parameters for the receiver,

optical fibre and lasers was presented and the analysis developed was based on those parame-

ters. The objective of this assessment was to verify the enhancement of a XG-PON system by

using APD receivers. Additionally, it was intended to study the the MPN effect on the final

solution.

Moreover, it was analysed the use of MLM lasers in both downstream and upstream direc-

tions. The MLM lasers cannot be employed due to the high dispersion suffered by the signal

emitted by an MLM laser.

Furthermore, it was analysed the use of the SLM lasers in the downstream direction and

in the upstream direction. In the downstream direction, the use of an APD instead of a PIN at

the ONU allows an improvement of reach and higher splitting ratio. Furthermore, the use of an

APD receiver allows the use of the common splitting ratios, between 1:8 and 1:64, for distances

of L “ 20 km and L “ 40 km. However, under the conditions studied, to achieve the common

splitting ratios in the upstream direction, the use of an APD receiver at the OLT is mandatory,

FEC needs to be employed and the emitting power of the ONU transmitter has to be increased.

Moreover, under the conditions studied, the splitting ratio of 1:128 was not achieved due to

68

6.2 Future work

limitations in the upstream direction.

6.2 Future work

Following the conclusions drawn above, some work topics for future investigation are suggested

in order to complement or continue the work accomplished in this dissertation:

• Study of the MPN impact in the coexistence of the GPON system and the video overlay

with the XG-PON system,

• Study of the MPN impact in the next-generation PON (NG-PON2).

69

6. CONCLUSION AND FUTURE WORK

70

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74

Appendix A

APD receiver sensitivity with finite extinc-

tion ratio

In this appendix, it is shown how the expression for the sensitivity of an APD receiver with

non-null extinction ratio is derived. The bit error ratio concept is introduced, leading to the

meaning of the receiver sensitivity. Furthermore, all the necessary steps taken to obtain the

sensitivity expression are described. Still, the obtained general expression for the APD receiver

sensitivity is applied to the case of a PIN receiver, considering unitary gain. Finally, it is derived

an approximated expression for the optimum avalanche gain of an APD receiver.

A.1 Bit error rate

The performance criterion of a digital receiver is the bit-error rate (BER). The BER is custom-

ary defined as the average probability of incorrect bit identification. Ergo, a BER of 1ˆ10´12

corresponds to an average of one error per 1012 bits transmitted. Usually, BER below of 10´9

is the required criterion for a digital receiver. The receiver sensitivity is then defined as the

minimum average power pi required for the receiver to operate with a designed value of BER.

So, in order to compute pi, BER must be calculated.

The sampled value I fluctuates from bit to bit around an average current value I0 or I1,

depending on whether the bit corresponds to 0 or 1 in the bit stream. The decision circuit com-

pares the sampled with a threshold current value ID: calls it bit 1 if I ą ID; calls it bit 0 if I ă ID.

Errors will occur if I ă ID for bit 1 or I ą ID for bit 0, due to receiver noise. Therefore, the BER

can be defined as

BER“ pp1qPp0{1q` pp0qPp1{0q, (A.1)

75

A. APD RECEIVER SENSITIVITY WITH FINITE EXTINCTION RATIO

where pp0q is the probability of receiving bit 0 and Pp1{0q is the probability of deciding 1 when

0 is received. The same for pp1q and Pp0{1q, mutatis mutandis. Assuming the probability of bit

0 equal to bit 1, as they are equally likely to occur, pp0q “ pp1q “ 1{2, BER becomes

BER“12pPp0{1q`Pp1{0qq . (A.2)

The probabilities Pp0{1q and Pp1{0q are very much dependent on the probability density func-

tion ppIq. The functional form of the probability density function ppIq depends on the statistics

of the noise sources responsible for current fluctuations. The shot noise and thermal noise are

well described by Gaussian statistics with zero mean and variances σ2s and σ2

c , respectively.

Note that this is true for PIN receivers. In the case of APD receivers, the shot noise being

treated as a Gaussian random variable is a common approximation, with a different expression

for the variance σ2s [19]. Since, statistically, the sum of two Gaussian random variables is itself

a Gaussian random variable, the variance of the probability density function of I is the sum of

the variances of the noises. Still, variances and average are different for each of the bits, so the

variances to take into account are σ20 and σ2

1. With that in mind, the conditional probabilities

are expressed by [19]

Pp0{1q “1

σ1?

2π

ż ID

´8

expˆ

´pI´ I1q

2

2σ21

˙

dI “12

erfcˆ

I1´ ID

σ1?

2

˙

, (A.3)

Pp1{0q “1

σ0?

2π

ż 8

ID

expˆ

´pI´ I0q

2

2σ20

˙

dI “12

erfcˆ

ID´ I0

σ0?

2

˙

, (A.4)

where erfc is the commonly used complementary error function [19] given by

erfcpxq “2?

π

ż 8

xexppý2

qdy. (A.5)

Replacing expressions A.3 and A.4 in the BER expression A.2 results in

BER“14

„

erfcˆ

I1´ ID

σ1?

2

˙

` erfcˆ

ID´ I0

σ0?

2

˙

. (A.6)

The expression A.6 shows the BER dependency of ID. In fact, in practice ID is optimized to

minimize BER, thus the minimum occurs when ID is chosen to verify

pID´ I0q2

2σ20

“pI1´ IDq

2

2σ21

` lnˆ

σ1

σ0

˙

. (A.7)

76

A.2 Preparatory steps

For most relevant cases, the last term may be neglected, which results in

pID´ I0q

σ0“pI1´ IDq

σ1” Q. (A.8)

For most PIN receivers, the decision threshold ID is placed in the middle ID “ pI0` I1q{2,σ1 “

σ0, since the noise domination factor is the thermal noise (σc " σs) and is independent of the

average current. For APD receivers, to set the decision threshold in order to minimize BER, the

explicit ID expression can be used

ID “σ0I1`σ1I0

σ0`σ1. (A.9)

Using expressions A.6 and B.27, the BER expression, only depending on the quality parameter

Q is given by

BER“12

erfcˆ

Q?

2

˙

«expp´Q2{2q

Q?

2π(A.10)

with Q parameter being obtained by expressions B.27 and A.9. The Q parameter is then given

by

Q“I1´ I0

σ1`σ0. (A.11)

For BER it was made an approximation by using the asymptotic expansion [19] of erfcpQ{?

2q

which is reasonably accurate for Q ą 3. Thus, since wanted values of BER are lower than

10´9 (which corresponds roughly to Q “ 5) and Q increases with the decrease of BER, the

approximation is valid.

A.2 Preparatory steps

The extinction ratio r is defined as quotient of the power when the light source is off (bit 0),

commonly defined as pi,0, and the power when the light source is on (bit 1), known as pi,1

r “pi,0

pi,1. (A.12)

It could, also, be defined as the inverse fraction rext “ pi,1{pi,0, though in that case it is com-

monly represented in dB, R “ 10logprextq “ 10logp1{rq. Once r is defined, it is possible to

77


define pi,0 and pi,1 as function of r and the total average incident power pi assuming [18]

pi “pi,0` pi,1

2“

pi,0`

1` 1r

˘

2ô 2pir “ pi,0pr`1q ô pi,0 “

2pirp1` rq

. (A.13)

Applying the same reasoning to pi,1

pi “pi,0` pi,1

2“

pi,1pr`1q2

ô pi,1 “2pi

p1` rq. (A.14)

The powers are currently in function of extinction ratio r, now it is necessary to search for the

relation of the received powers and the quality parameter Q. Expression A.11 is actually the key.

In the numerator part of the quotient, there are the average currents for bits 0 and 1. The average

current can be related to the power of the correspondent bit using the relation pi“ Ip{RλAPD , with

RλAPD “RλM. Rλ is the unitary gain responsivity and M is the APD avalanche gain. Substituting

I0 and I1 on equation A.11

Q“MRλppi,1´ pi,0q

σ1`σ0“

MRλp2pip1`rq ´

2pirp1`rqq

σ1`σ0“p1´ rqp1` rq

2MRλ pi

σ1`σ0. (A.15)

The expression A.15 is now closer to the objective, which is to achieve the expression for the

sensitivity (pi) varying with Q for any extinction ratio. Although, the square root of the noise

variance of bit 0 (or 1 is also dependent on the respective power pi,0 (or pi,1). The noise variance

of any given bit depends on the thermal noise and the shot noise of such bit [19]. The thermal

noise is independent of the power as it occurs in the receiver circuitry. Then, the shot noise is

the component responsible for the dependency of the respective associated average power. The

square root noise variances for bits 0 and 1 are described as follows

σ0 “

c

´

σ2s,0`σ2

c

¯

, (A.16)

σ1 “

c

´

σ2s,1`σ2

c

¯

. (A.17)

The shot noise variances of bits 0 and 1 are given by

σ2s,0 “ 2qM2FApMqpRλ pi,0` IdqBe,n “ 2qM2FApMqBe,n

ˆ

Rλ

2pirp1` rq

` Id

˙

, (A.18)

78

A.3 Deriving APD sensitivity expression

σ2s,1 “ 2qM2FApMqpRλ pi,1` IdqBe,n “ 2qM2FApMqBe,n

ˆ

Rλ

2pi

p1` rq` Id

˙

. (A.19)

As mentioned, the thermal noise is not dependent on the power so, it is independent of the

receiver being a PIN or an APD. Also, from the computation perspective, it would introduce

more parameters to take into account, so there is no need to replace σ2c for its expression.

The shot noise expression introduces another level of dependency, as the shot noise on

APD is also affected by another term: the excess noise factor FApMq [19] given by

FApMq “ kAM`p1´ kAqp2´1{Mq. (A.20)

Nevertheless, there is no need for substituting this additional noise factor for its expression A.20

in the shot noise expression as it will complicate even more the steps towards the result and,

ultimately, it could not simplify the result. So, it will be treated as another variable. With all

variables in (A.11) scrutinized, starting to derive the expression in order to pi is the next step.

A.3 Deriving APD sensitivity expression

The natural course of action would be to replace σ1 and σ0 in expression A.15 and compute the

result from there. That will make A.15 a very big expression. Ergo, some auxiliary variables

will be created instead, aggregating some of the variables that repeat, (such as the responsivity

or the effective noise bandwidth). That way the expression is more simple to be comprehended

and more readable. Let n be

n“ 2MRλ

p1´ rqp1` rq

(A.21)

and u be

u“ 2qM2FApMqBe,n. (A.22)

These help variables just created, are then applied in the shot noise variance expression, result-

ing in

Q“npi

c

´´

Rλ2pip1`rq ` Id

¯

u`σ2c

¯

`

c

´´

Rλ2pirp1`rq ` Id

¯

u`σ2c

¯

. (A.23)

Solving this expression by hand is very laborious due to its number of variables (even if the

auxiliary variables created are not replaced by their corresponding expression). Hence, the

whole expression was introduced into MATLAB, replacing the auxiliary variables for their val-

79


ues, leading to the complete full expression. Such expression was then passed as an argument

to the MATLAB function solve, which solved the expression in order to pi variable, as wished.

Two solutions were obtained, solution one

pi “Qpr`1q

MRλpr´1q2

„

QqFApMqMBe,npr`1q

`

b


(A.24)

and solution two

pi “Qpr`1q

MRλpr´1q2

„

QqFApMqMBe,npr`1q

´

b


. (A.25)

The aimed solution has to have certain characteristics thus, some limitations must be imposed.

Therefore, to determine which of the solutions is the correct one, a simple imposition is made.

Since pi corresponds to a power value, physically only positive values have meaning. Thus, the

chosen solution must be always positive, in the operation domain (M ą 0).

A simple procedure for analysing both solutions consists in plotting the two functions, using

Q r Rλ [A/W] Be,n [GHz] σ2c [A2] Id [nA] kA

7 0.152 0.73 8 p100ˆ10´9q2 100 0.9

Table A.1: Set of typical values for sensitivity parameters for testing the two sensitivity solutions.

typical parameters Table A.1 and making M varying in the wanted domain. It is possible to

see, after examination of the procedure result shown in Fig. A.1, that solution two has negative

values for the sensitivity. That violates the simple imposition made, as it is not physically

possible. Ergo, solution two is excluded, leaving solution one expression A.24, as the correct

solution.

80

A.4 APD sensitivity applied to PIN

5 10 15 20 25 30−150

−100

−50

0

50

100

150

Avalanche Gain (M)

Sen

sitiv

ity (µ

W)

Solution 1Solution 2

Figure A.1: Sensitivity values for both solutions presented.

A.4 APD sensitivity applied to PIN

The sensitivity obtained expression A.24 is also valid for a PIN diode receiver, (considering

a PIN as a unitary gain APD M “ 1). The value of FApMq in that case is 1, as displayed by

expression A.26.

FApMq “ kA`p1´ kAqp2´1q “ kA´ kA`1“ 1. (A.26)

Hence, the final expression for a PIN is given by

pi “Qpr`1q

MRλpr´1q2

„

QqFApMqMBe,npr`1q

`

b


“Qpr`1q

Rλpr´1q2

„

QqBe,npr`1q`b


(A.27)

A.5 Deriving the APD optimum gain

By inspecting Fig. A.1, due to the evolving pattern of the sensitivity curve (solution 1), there is

indication that only one value of M optimizes the sensitivity. When that gain value is reached,

the maximum sensitivity is achieved. As so, theoretically the optimum gain can be obtained

by following a series of steps: differentiating the expression A.24 in order to M; After the

differentiation is complete, the differentiated expression is equalized to zero; Then, the result

expression is solved in order to the avalanche gain M, obtaining the expression for the optimum

81


gain MOptimum for an APD, regardless of the APD parameters.

Yet, after recurring to computer tools, due to the nature of the expression, it was concluded

that a simple direct formula could not be achieved. Approximations had to be implemented.

If the square root in expression A.24 is disregarded, inside the parenthesis there are three

visible distinct terms. Though, it is not quite easy to understand which of the terms may or

may not be neglected without great influence on the final result. So, in order to better under-

stand the contribution of each of the identifiable terms, expression 3.18 was subdivided in three

components A.28, A.29 and A.30 that do not necessarily add up to form the original expression.

pi,A “Qpr`1q

MRλpr´1q2rQpr`1qqFApMqMBe,ns (A.28)

pi,B “Qpr`1q

MRλpr´1q2

„

b

p2qFApMqM2Be,nId`σ2cqpr´1q2

(A.29)

pi,C “Qpr`1q

MRλpr´1q2

„

b

rp2QqFApMqMBe,nq2

(A.30)

Using the parameters of Table A.1, the three components were compared against the original

expression with the purpose to evaluate which term has an negligible contribution, when com-

pared against the other two. The comparison was made for a wide range of avalanche gain

values. However the focus should be in the area where the sensitivity reaches its minimum,

which is the relevant area, since it corresponds to the optimum gain. Also, the approximation

must be valid within the goal domain, which comprehends extinction ratio values between 0

and 0.152 (maximum imposed by ITU-T)[17].

The analysis of Fig. A.2, leads to the conclusion that the component pi,C A.30 is least

significant when compared with the other two. Thus, it is the most suitable to be neglected.

However Fig. A.2 is for an extinction ratio of 0.152. In order to proceed further, it is necessary

to evaluate whether the extinction ratio influences this result or not. Therefore, two other values

were chosen to represent the goal extinction ratio domain. An extinction ratio of 0.1 and an

extinction ratio of 0.05. The plots for the additional two extinction ratios are in Fig. A.3 and

Fig. A.4 for r “ 0.1 and r “ 0.05, respectively.

The results shown in Fig. A.3 and Fig. A.4 prove the validity of the whole procedure,

since the approximation is valid within the wanted extinction ratio range.

Nevertheless, the approximation accomplished by neglecting the component pi,C is still

insufficient. Further approximations must be made in order to obtain an expression for the op-

82

A.5 Deriving the APD optimum gain

5 10 15 20 25 30 35 40−45

−40

−35

−30

−25

−20

Avalanche Gain (M)

dBm

pi

pi,A

pi,B

pi,C

Figure A.2: Sensitivity expression compared against its three components for an extinction ratio of0.152 .

5 10 15 20 25 30 35 40−45

−40

−35

−30

−25

−20

Avalanche Gain (M)

dBm

pi

pi,A

pi,B

pi,C


timum gain of the APD receiver. The dark current Id , which is typically very small, could be

considered zero. Thus, simplifying the expression enough so that an expression can be achieved.

Following the implemented approximations, the resulting expression is given by

pi,apx “Qpr`1q

MRλpr´1q2

„

Qpr`1qqFApMqMBe,n`

b

σ2cpr´1q2

. (A.31)

Following the steps enumerated earlier, the sensitivity approximated expression A.31 was dif-

ferentiated, recurring to MATLAB. The resulting differentiated expression was then equalized

83


5 10 15 20 25 30 35 40−45

−40

−35

−30

−25

−20

Avalanche Gain (M)

dBm

pi

pi,A

pi,B

pi,C


to zero and solved in order to the avalanche gain M. The resultant approximated expression for

computing the optimum gain for an APD receiver, given any set of parameters, is then given by

MOptimum “

c

Be,nQqkApr`1q”

a

σ2cpr´1q2`pkApr`1q´ r´1qBe,nQq

ı

Be,nQqkApr`1q. (A.32)

84

Appendix B

Auxiliary derivations related to MPN

B.1 BER in SLM lasers

Due to the nature of the nearly single-mode lasers behaviour, its partition mode fluctuations

cannot be treated as a Gaussian random variable. Actually, it has been observed that its proba-

bility density function exhibits a exponential distribution behaviour [28]. In order to calculate

the BER, it is necessary to add the contribution of the shot and thermal noises, whose proba-

bility density functions are well approximated by Gaussian distributions, and the contribution

from the MPN noise, which, as stated, follows an exponential distribution.

Considering the total noise current to be inptq, the Gaussian noise current to be iGptq and the

exponential noise current be iexpptq

inptq “ iGptq` iexpptq. (B.1)

Let us consider that bits 0 and 1 are two different random variables iG0ptq and iG1ptq, respec-

tively. Thus, iG0ptq and iG1ptq have different standard deviations and, therefore, different proba-

bility distributions . The corresponding probability density functions of iG0ptq, iG1ptq and iexpptq

are, respectively

pG0pxq “1

σ0?

2πexp

ˆ

´x2

2σ20

˙

. (B.2)

pG1pxq “1

σ1?

2πexp

ˆ

´x2

2σ21

˙

. (B.3)

pexppyq “

$

’

&

’

%

1b

exp´

ýb

¯

, yě 0

0, yă 0(B.4)

85

B. AUXILIARY DERIVATIONS RELATED TO MPN

where σ0 and σ1 are the standard deviation of the receiver noise for bits 0 and 1, respectively,

and b characterizes the MPN noise. Let iG0,1ptq be the noise Gaussian distribution for either

bit 0 or 1. Since iG0,1ptq and iexpptq are statistically independent, their joint density probability

function pG0,1,exppx,yq is simply the product of the two individual probability density functions

pG0,1,exppx,yq “ pG0,1pxqpexppyq. (B.5)

Let the signal current for bit 0 and 1 be I0 and I1, respectively. The receiver will incur in an

error when the total noise current inptq added to the signal current, I0 or I1, induces a mistake in

the receiver’s decision. Let ID be the receiver’s threshold, BER can be defined as

BER“ PpI ą IDqPp0q`PpI ă IDqPp1q. (B.6)

The value of I is different for each bit, hence each bit can be attributed a different threshold

related to ID as follows

I “ iGptq` iexpptq ě ID0 “ ID´ I0, (B.7)

I “ iGptq` iexpptq ď ID1 “ ID´ I1. (B.8)

Thus, considering the bits 0 and 1 equally probable, BER is given by

BER“ PpI ą ID0qPp0q`PpI ă ID1qPp1q

“12rPpI ą ID0q`PpI ă ID1qs

(B.9)

The probability PpI ą ID0q is obtained when pG,exppx,yq is integrated over the plane region of

(x,y) where x` yą ID0 . Due to its distribution, y will be zero for values under zero. Hence, the

integration area can be divided in two sub areas as shown in Fig. B.1: (1) plane region delimited

by the lines defined by x` y“ ID0 e x“ ID0 ; (2) plane region delimited by the lines defined by

x“ ID0 e y“ 0. In region (1),´8ď xď ID0 and ID0´xď yď`8. In region (2), ID0 ď xď`8

and 0ď yď`8. Thus, the probability PpI ą ID0q is given by

PpI ą ID0q “

ĳ

x`yąID0

pG,exppx,yqdxdy

“

ż ID0

´8

ż `8

ID0´xpexppyqdy pGpxqdx`

ż `8

ID0

ż `8

0pexppyqdy pGpxqdx .

(B.10)

86


ID0

ID0

x

y

x + y = ID0

Figure B.1: Regions of integration of PpI ą ID0q.

Since pexppyq corresponds to the probability density function

ż `8

0pexppyqdy“ 1, (B.11)

andż `8

ID0´xpexppyqdy“

ż `8

ID0´x

1b

exp´

ýb

¯

dy“ expˆ

x´ ID0

b

˙

. (B.12)

The probability PpI ą ID0q is then defined by

PpI ą ID0q “

ż ID0

´8

expˆ

x´ ID0

b

˙

pGpxqdx`ż `8

ID0

pGpxqdx. (B.13)

In optical communications, a well known function which is commonly used is the Qpuq func-

tion. Qpuq given by

Qpuq “1?

2π

ż 8

uexp

ˆ

´γ2

2

˙

dγ

“1?

2π

ˆ

c

π

2erfc

ˆ

u?

2

˙˙

“12

erfcˆ

u?

2

˙

.

(B.14)

The function Qpuq can be used to simplify the integral calculation of PpI ą ID0q. However, in

order to do that, a variable substitution must be applied for the exponential argument to match

87


´γ

2 . In the case of PpI ą ID0q, a substitution can be made by defining γ as

γ“xσ´

σ

b, (B.15)

using

dγ“1σ

dx. (B.16)

Applying the variable substitution to B.13

PpI ą ID0q “

ż ID0

´8

expˆ

x´ ID0

b

˙

pGpxqdx`ż `8

ID0

pGpxqdx.

“

exp´

ÍD0b

¯

?2π

ż ID0

´8

1σ0

expˆ

´x2

2σ20`

xb´

σ20

2b2 `σ2

02b2

˙

dx`1?

2π

ż `8

ID0

1σ0

expˆ

´x2

2σ20

˙

dx

“

exp´

ÍD0b `

σ20

2b2

¯

?2π

ż

ID0σ0´

σ0b

´8

expˆ

´γ2

2

˙

dγ`1?

2π

ż `8

ID0{σ0

expˆ

´γ2

2

˙

dγ

“ expˆ

ÍD0

b`

σ20

2b2

˙„

1´Qˆ

ID0

σ0´

σ0

b

˙

`Qˆ

ID0

σ0

˙

.

(B.17)

On the other hand, the probability PpI ă ID1q implies that x` y ď ID1 . As before, y is zero for

ID0

ID0

x

y

x + y = ID0

Figure B.2: Region of integration of PpI ă ID1q.

values under zero. The integration area is defined by the region plane contained by the lines

defined by x`y“ ID1 and y“ 0, as shown in Fig. B.2 . With 0ď yď ID1´x and´8ď xď ID1 .

88


PpI ă ID1q is given by

PpI ă ID1q “

ĳ

x`yăID1

pG,exppx,yqdxdy

“

ż ID1

´8

ż ID1´x

0pexppyqdy pGpxqdx

“

ż ID1

´8

„

1´ expˆ

x´ ID1

b

˙

pGpxqdx.

(B.18)

In order to use Qpuq to simplify the integral calculation of PpI ă ID1q, a variable substitution

must be applied for the exponential argument to match´ γ

2 . In the case of PpI ă ID1q the variable

substitution can be accomplished by defining γ as

γ“xσ, (B.19)

using

dγ“1σ

dx. (B.20)

Applying the variable substitution to B.18

PpI ă ID1q “

ż ID1

´8

„

1´ expˆ

x´ ID1

b

˙

pGpxqdx

“

ż ID1

´8

pGpxqdx´ż ID1

´8

expˆ

x´ ID1

b

˙

pGpxqdx

“ 1´Qˆ

ID1

σ1

˙

´ expˆ

ÍD1

b`

σ21

2b2

˙„

1´Qˆ

ID1

σ1´

σ1

b

˙

.

. (B.21)

The BER is then given by

BER“12

„

expˆ

ÍD0

b`

σ20

2b2

˙„

1´Qˆ

ID0

σ0´

σ0

b

˙

`Qˆ

ID0

σ0

˙

` 1´Qˆ

ID1

σ1

˙

´ expˆ

ÍD1

b`

σ21

2b2

˙„

1´Qˆ

ID1

σ1´

σ1

b

˙

.

(B.22)

Previously, the b value of expression B.4 was left undefined. The value of b characterizes the

MPN noise, so it is necessary to define it. The nature of a single-mode laser is quantified by the

mode suppression ration (SMSR), which is defined as the ratio of the main mode power Pmm

and the most dominant side mode power Psm. The MPN noise in a nearly single-mode laser

is related to the fluctuations of the power of the side mode. The side mode power follows a

89


exponential distribution given by [28]

pexppPsmq “1¯Psm

expˆ

´Psm

¯Psm

˙

(B.23)

where ¯Psm is the average value of the random variable Psm. If the total power remains constant

[30], let us assume that the total power α“ Psm`Pmm. Then, the main mode power distribution

is given by [28]

pexppPsmq “1¯Psm

expˆ

´pα´Psmq

¯Psm

˙

. (B.24)

In this analysis, it was considered the noise currents. Thus, the MPN noise must be characterized

in terms of powers, so that the analysis is consistent. Therefore, the side mode current follows

an exponential distribution given by

pexppIsmq “1¯Ism

expˆ

Ísm¯Ism

˙

(B.25)

where ¯Ism is the average side mode current. The power of the side mode is not sensitive to the

carrier density fluctuations [30]. Thus, bits 0 and 1 will have the same average value for the

side mode current Ism. Let us consider b “ ¯Ism as the average side mode current. Substituting

b for the corresponding value in expression B.22, taking into account that ID0 “ ID´ I0 and

ID1 “ ID´ I1 and using erfc leads to BER being given by

BER“12

„

expˆ

´pID´ I0q

Is`

σ20

2Is2

˙„

1´12

erfcˆ

Q?

2´

σ0?

2Is

˙

`12

erfcˆ

Q?

2

˙

` 1´12

erfcˆ

´Q?

2

˙

´ expˆ

´pID´ I1q

Is`

σ21

2Is2

˙„

12

erfcˆ

Q?

2`

σ1?

2Is

˙(B.26)

where Q is given bypID´ I0q

σ0“pI1´ IDq

σ1” Q (B.27)

and ID is the current decision threshold. The current I may be rewritten in order to the respective

power using Eq. 3.2. Since we are considering the APD receiver, the gain factor must be added.

The current is given by

I “ PRλM. (B.28)

90


In order to further simplify the expression B.26, the given formula can be used

erfcpxq´ erfcp´xq “ ´2erfpxq “ ´2`2erfcpxq. (B.29)

Using the result in formula B.29, a part of expression B.26 can be simplified as follows

12

erfcˆ

Q?

2

˙

`1´12

erfcˆ

´Q?

2

˙

“ 1`12

„

´2`2erfcˆ

Q?

2

˙

“ erfcˆ

Q?

2

˙

. (B.30)

Using the simplification accomplished in Eq. B.30 and substituting on expression B.26 every

current by the corresponding power, using Eq. B.28, the BER is given by

BER“12

„

expˆ

´pPD´ P0q

¯Psm`

σ20

2p ¯PsmRλMq2

˙„

1´12

erfcˆ

Q?

2´

σ0?

2p ¯PsmRλMq

˙

` erfcˆ

Q?

2

˙

´ expˆ

´pPD´ P1q

¯Psm`

σ21

2p ¯PsmRλMq2

˙„

12

erfcˆ

Q?

2`

σ1?

2p ¯PsmRλMq

˙

(B.31)

where P0 is the average power of bit 0, P1 the average power of bit 1 and PD is the power

decision threshold. Applying the SMSR concept from Eq. 4.3 to expression B.31, BER is given

by

BER“12

«

exp

˜

´pPD´ P0qSMSR

P0`

SMSR2σ2

02pP0RλMq2

¸

„

1´12

erfcˆ

Q?

2´

SMSRσ0?

2pP0RλMq

˙

` erfcˆ

Q?

2

˙

´ exp

˜

´pPD´ P1qSMSR

P1`

SMSR2σ2

12pP1RλMq2

¸

„

12

erfcˆ

Q?

2`

SMSRσ1?

2pP1RλMq

˙

ff

(B.32)

B.1.1 BER particular cases

Consider a PIN receiver (M “ 1) with a unitary responsivity (Rλ “ 1A/W). Also, consider a null

extinction ratio (r “ 0) and the decision threshold set at Pmm{2, where Pmm is the average main

mode power and Psm is the average power of the side mode. In this case, P0 “ 0 and P1 “ Pmm.

91


Therefore, the BER is given by

BER“12

„

expˆ

´Pmm

2Psm`

σ20

2P2sm

˙„

1´12

erfcˆ

Q?

2´

σ0?

2Psm

˙

` erfcˆ

Q?

2

˙

´ expˆ

Pmm

2Psm`

σ21

2P2sm

˙„

12

erfcˆ

Q?

2`

σ1?

2Psm

˙

.

(B.33)

Due to the approximations used, I “MRλP« P, thus σ0 and σ1 can be rewritten as follows

Q“ID´ I0

σ0“

PD´P0

σ0ô σ0 “

PD´P0

Q“

Pmm

2Q, (B.34)

Q“I1´ ID

σ1“

P1´PD

σ1ô σ1 “

P1´PD

Q“

Pmm

2Q. (B.35)

The ratio between the average power of the main mode and the average power of side mode is

the mode suppression ratio SMSR“ Pmm{Psm. Thus, the BER is given by

BER“12

„

expˆ

´SMSR

2`

SMSR2

8Q2

˙„

1´12

erfcˆ

Q?

2´

SMSR2?

2Q

˙

` erfcˆ

Q?

2

˙

´ expˆ

SMSR2

`SMSR2

8Q2

˙„

12

erfcˆ

Q?

2`

SMSR2?

2Q

˙

.

(B.36)

The BER expression B.36 can be simplified even further. Let us consider both erfc arguments

in expression B.36. Let us consider the first argument a “ Q?2´ SMSR

2?

2Qand the second b “

Q?2` SMSR

2?

2Q. For the values of Q and SMSR used in optical telecommunications, typically

Q ą 3 and SMSR ą 30 dB, erfcpaq « 2 and erfcpbq « 0. In fact, if Q “ 3 and SMSR “ 30 dB,

a « ´1.41 and b « 5.66 which means erfcpaq " erfcpbq. The erfc(x) function has the limits of

erfcp´8q “ 2 and erfcp`8q “ 0. Therefore, since erfcpbq is negligible, the BER expression

for a PIN receiver with null extinction ratio is given by

BER“12

erfcˆ

Q?

2

˙

`12

expˆ

´SMSR

2`

SMSR2

8Q2

˙„

1´12

erfcˆ

Q?

2´

SMSR2?

2Q

˙

. (B.37)

The obtained expression B.37 is similar to the BER expression shown in Eq. 5.4.10 of [19] in

page 208, for a PIN receiver. Thus, confirming its application to a well known case.

92

B.2 BER in SLM lasers based on Gaussian approximation


The analysis presented in section B.1 does not account for the fluctuations in the laser main

mode current. The fluctuations in the laser mode current also contribute to the noise current and

can have influence on the detected bit by the receiver. The main mode current i0,1ptq, for bit 0

or 1, can be considered a random variable with an associated statistical distribution. If the two

mode laser is considered, the total current after the optical receiver is then given by

iT0,1ptq “ i0,1ptq` isptq (B.38)

where isptq corresponds to the current after the optical receiver resulting of the side-mode .

It is known [31] that the total laser current iT0,1ptq follows a Gaussian distribution. Thus,

the probability density function for iT0,1ptq is given by

pT0,1pxq “1

σT0,1

?2π

exp

˜

´px´ IT0,1q

2

2σ2T0,1

¸

. (B.39)

where IT0,1 is the total average current for bit 0 or 1 and σT0,1 is the standard deviation of the

total current for bit 0 or 1.

We may define the total current as iT0,1ptq “ IT0,1`δiT0,1ptq, where only δiT0,1ptq is a random

variable and corresponds to the fluctuations of the total current. Hence, the probability density

function for δiT0,1ptq is given by

pδT0,1pxq “1

σT0,1

?2π

exp

˜

´x2

2σ2T0,1

¸

. (B.40)

B.2.1 BER derivation

Considering the probability of bit 0 and 1 to be equal, the BER is given by

BER“ PpiT0ptq` iG0ptq ą IDqPp0q`PpiT1ptq` iG1ptq ă IDqPp1q. (B.41)

Then, the BER is

BER“12rPpδiT0ptq` iG0ptq ą ID´ IT0 “ ID0q`PpδiT1ptq` iG1ptq ă ID´ IT1 “ ID1qs (B.42)

93


where iG0,1ptq corresponds to the Gaussian noise current for bits 0 or 1, and ID is the decision

threshold. The Gaussian noise currents iG0ptq and iG1ptq have also Gaussian probability density

functions represented by Eqs. B.2 and B.3, respectively. Let Zptq “ δiT0,1ptq` iG0,1ptq be the

sum of the current at the receiver resulting from the laser power and the Gaussian current. Since

δiT0,1ptq and iG0,1ptq are statistically independent, and both are Gaussian random variables, the

probability density function of Zptq is given by

pZpzq “1

c

2π

´

σ2T0,1`σ2

G0,1

¯

exp

¨

˝´pz´pµT0,1`µG0,1qq

2

2´

σ2T0,1`σ2

G0,1

¯

˛

‚ (B.43)

where µT0,1 and µG0,1 correspond to the mean of the random variables δiT0,1ptq and iG0,1ptq, re-

spectively, and σT0,1 and σG0,1 correspond to the standard deviation of the random variables

δiT0,1ptq and iG0,1ptq, respectively. Both random variables δiT0,1ptq and iG0,1ptq have null mean,

hence, PpZptq ą ID0q is given by

PpZptq ą ID0q “

ż

ząID0

pZpzqdz

“

ż `8

ID0

1c

2π

´

σ2T0`σ2

G0

¯

exp

¨

˝´z2

2´

σ2T0`σ2

G0

¯

˛

‚dz

“12

»

—

—

–

1´ erf

¨

˚

˚

˝

ID0c

2´

σ2T0`σ2

G0

¯

˛

‹

‹

‚

fi

ffi

ffi

fl

“12

erfc

¨

˚

˚

˝

ID0c

2´

σ2T0`σ2

G0

¯

˛

‹

‹

‚

.

(B.44)

94


Applying the same reasoning, PpZptq ă ID1q is given by

PpZptq ă ID1q “

ż

zăID1

pZpzqdz

“

ż ID1

´8

1c

2π

´

σ2T1`σ2

G1

¯

exp

¨

˝´z2

2´

σ2T1`σ2

G1

¯

˛

‚dz

“12

»

—

—

–

1` erf

¨

˚

˚

˝

ID1c

2´

σ2T1`σ2

G1

¯

˛

‹

‹

‚

fi

ffi

ffi

fl

“ 1´12

erfc

¨

˚

˚

˝

ID1c

2´

σ2T1`σ2

G1

¯

˛

‹

‹

‚

“12

erfc

¨

˚

˚

˝

pÍD1qc

2´

σ2T1`σ2

G1

¯

˛

‹

‹

‚

.

(B.45)

Substituting the results of expressions B.44 and B.45 in expression B.42, BER is given by

BER“14

»

—

—

–

erfc

¨

˚

˚

˝

ID0c

2´

σ2T0`σ2

G0

¯

˛

‹

‹

‚

` erfc

¨

˚

˚

˝

pÍD1qc

2´

σ2T1`σ2

G1

¯

˛

‹

‹

‚

fi

ffi

ffi

fl

. (B.46)

In order to evaluate the influence of the MPN, introduced by the SLM laser, on BER, the

expression must be rewritten in terms of the laser side-mode ratio SMSR parameter. Let

IT0,1 “ I0,1` Ism and SMSR “ Imm{Ism, where Imm is the total current after the optical receiver

resulting from the laser main mode. Expression B.46 can be rewritten, leading to BER given by

BER“14

»

—

—

–

erfc

¨

˚

˚

˝

ID´ I0Ímm

SMSRc

2´

σ2T0`σ2

G0

¯

˛

‹

‹

‚

` erfc

¨

˚

˚

˝

I1Ìmm

SMSR ´ IDc

2´

σ2T1`σ2

G1

¯

˛

‹

‹

‚

fi

ffi

ffi

fl

. (B.47)

Normally, ID is chosen to minimize BER, the minimum occurs when ID is chosen such that

´

ID´ I0Ímm

SMSR

¯2

2´

σ2T0`σ2

G0

¯ “

´

I1Ìmm

SMSR ´ ID

¯2

2´

σ2T1`σ2

G1

¯ ` ln

˜

σ2T1`σ2

G1

σ2T0`σ2

G0

¸

. (B.48)

95


Assuming that the last term in expression B.48 is negligible in most cases, yields that ID can be

obtained by´

ID´ I0Ímm

SMSR

¯

b

σ2T0`σ2

G0

“

´

I1Ìmm

SMSR ´ ID

¯

b

σ2T1`σ2

G1

(B.49)

An explicit expression for ID is given by

ID “

b

σ2T1`σ2

G1

´

I0Ìmm

SMSR

¯

`

b

σ2T0`σ2

G0

´

I1Ìmm

SMSR

¯

b

σ2T0`σ2

G0`

b

σ2T1`σ2

G1

(B.50)

The BER with the optimum setting of the threshold is obtained by using expressions B.47 and

B.49. The resulting BER expression is given by

BER“14

erfcˆ

Q?

2

˙

`14

erfcˆ

Q?

2

˙

“12

erfcˆ

Q?

2

˙

«expp´Q2{2q

Q?

2π

(B.51)

where the Q parameter is obtained from expressions B.49 and B.50 and is given by

Q“I1´ I0

b

σ2T0`σ2

G0`

b

σ2T1`σ2

G1

. (B.52)

The bit noise variances σ2G0

and σ2G1

are given by expressions A.16 and A.17, respectively.

Throughout this section it was considered that bit 0 and bit 1 are equally likely to occur. Based

on that assumption, the average power of the main mode Imm may be defined as

Imm “12

I0`12

I1. (B.53)

The variance of the total current after the receiver σTi for bit i is obtained by computing the

value of Var(Imm + Ism). Since the random variables that represent the main mode current and

the side mode current are not independent, the variance is given by

VarpImm` Ismq “ VarpImmq`VarpIsmq`2CovpImm, Ismq. (B.54)

96


The covariance CovpImm, Ismq is given by

CovpImm, Ismq “ E rImmIsmsÉ rImmsE rIsms . (B.55)

Let us consider mspnq “ E rInsms and mpnq “ E rIn

T s, the expected value E rImmIsms is given by

E rImmIsms “

ż `8

0xpspxq

ż `8

´xypT px` yq dy dx

“

ż `8

0xpmp1q´ xq pspxq dx

“ msp1qmp1q´msp2q

“ E rIsmsE rIsÉ“

I2sm‰

.

(B.56)

Since E rIs “ E rImmsÈ rIsms, E rIsms “ Is the covariance CovpImm, Ismq is then given by

CovpImm, Ismq “ E rImmIsmsÉ rImmsE rIsms

“ E rIsmsE rImmsÈ rIsmsE rIsmsÉ“

I2sm‰

É rImmsE rIsms

“ pE rIsmsq2É

“

I2sm‰

“´VarpIsmq.

(B.57)

The variance of the total current after the receiver σ2Ti

for bit i is then given

σ2Ti“ σ

2mmi´σ

2smi

(B.58)

where the variance of the laser intensity noise σ2mmi

is given by

σ2mmi

“ RλMPirl (B.59)

where Pi is the power of bit i and the parameter rl is a measure of the noise level of the incident

optical signal. The parameter rl is considered as the inverse of the SNR of the light emitted by

the transmitter [19]. Typically, the transmitter SNR is better than 20 dB and rl ă 0.01 [19]. The

side-mode noise variance is given by

σ2smi“

ˆ

RλMPi

SMSR

˙2

(B.60)

97


B.3 Validation of the model used to obtain BER

The BER expression 4.30 requires further analysis and is only usable if proven valid. In [32],

it is presented a more complex model in which the total current follows the non-central chi-

squared distribution with two degrees of freedom given by

pT0,1pxq “1

2ψexp

ˆ

´x`12ψ

˙

I0

ˆ?x

ψ

˙

(B.61)

where ψ is the distribution parameter and I0 is the modified zero-order Bessel function of the

first kind. In order to compare the Gaussian distribution approximation to the non-central chi-

squared distribution on Eq. B.61, the variance and and mean of the chi-squared must be ob-

tained. The relation between ψ and σGaussian is given by

σ2Gaussian “ 4ψp1`ψq. (B.62)

The mean value of the non-central chi-squared in expression B.61 is given by

µ“ 1`2ψ. (B.63)

Using the value of ψ “ 2ˆ10´4 [32], expressions B.62 and B.64 were used to compute the σ

and µ parameters of a Gaussian distribution. The two probability density functions comparison

is shown in Fig. B.3. For ψ“ 2ˆ10´4, it is shown in Fig. B.3 that the Gaussian distribution is

a good approximation to the chi-squared distribution.

In [31], the Gaussian distribution is proposed as a representation of the total current and

a value of σGaussian “ 0.045, measured experimentally, was used. The value σGaussian “ 0.045

leads to ψ « 5.0625ˆ10´4. It is shown in Fig. B.4 the comparison between the two distribu-

tions using ψ“ 5.0625ˆ10´4.

Again, the comparison on Fig. B.4 shows that the Gaussian distribution is a good approx-

imation. From the formulation in [32], the relation between ψ and SMSR is given by

ψ«1

2SMSR. (B.64)

Thus, the results presented in Figs. B.3 and B.4 correpond to values of SMSR « 34 dB and

SMSR « 30 dB, respectively. Since ITU-T recommends values of SMSR above 30 dB, it can

98

B.3 Validation of the model used to obtain BER

Noncentral Chi−squared ModelGaussian Model

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

−15

−14

−13

−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

0

1

2

3

4

x

log(f

(x))

Figure B.3: Gaussian distribution and noncentral Chi-squared distribution for ψ“ 2ˆ10´4 .

Noncentral Chi−squared ModelGaussian Model

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

−15

−14

−13

−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

0

1

2

3

4

x

log(f

(x))

Figure B.4: Gaussian distribution and noncentral Chi-squared distribution for ψ“ 5.0625ˆ10´4.

be concluded that the non-central chi-squared distribution is well approximated by the Gaussian

distribution.

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